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<?php |
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namespace PhpOffice\PhpSpreadsheet\Calculation; |
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use PhpOffice\PhpSpreadsheet\Shared\Trend\Trend; |
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class Statistical |
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{ |
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const LOG_GAMMA_X_MAX_VALUE = 2.55e305; |
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const XMININ = 2.23e-308; |
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const EPS = 2.22e-16; |
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const MAX_VALUE = 1.2e308; |
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const MAX_ITERATIONS = 256; |
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const SQRT2PI = 2.5066282746310005024157652848110452530069867406099; |
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private static function checkTrendArrays(&$array1, &$array2) |
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{ |
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if (!is_array($array1)) { |
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$array1 = [$array1]; |
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} |
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if (!is_array($array2)) { |
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$array2 = [$array2]; |
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} |
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$array1 = Functions::flattenArray($array1); |
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$array2 = Functions::flattenArray($array2); |
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foreach ($array1 as $key => $value) { |
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if ((is_bool($value)) || (is_string($value)) || ($value === null)) { |
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unset($array1[$key], $array2[$key]); |
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} |
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} |
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foreach ($array2 as $key => $value) { |
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if ((is_bool($value)) || (is_string($value)) || ($value === null)) { |
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unset($array1[$key], $array2[$key]); |
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} |
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} |
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$array1 = array_merge($array1); |
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$array2 = array_merge($array2); |
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return true; |
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} |
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/** |
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* Incomplete beta function. |
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* |
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* @author Jaco van Kooten |
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* @author Paul Meagher |
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* |
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* The computation is based on formulas from Numerical Recipes, Chapter 6.4 (W.H. Press et al, 1992). |
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* |
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* @param mixed $x require 0<=x<=1 |
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* @param mixed $p require p>0 |
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* @param mixed $q require q>0 |
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* |
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* @return float 0 if x<0, p<=0, q<=0 or p+q>2.55E305 and 1 if x>1 to avoid errors and over/underflow |
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*/ |
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private static function incompleteBeta($x, $p, $q) |
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{ |
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if ($x <= 0.0) { |
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return 0.0; |
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} elseif ($x >= 1.0) { |
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return 1.0; |
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} elseif (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > self::LOG_GAMMA_X_MAX_VALUE)) { |
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return 0.0; |
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} |
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$beta_gam = exp((0 - self::logBeta($p, $q)) + $p * log($x) + $q * log(1.0 - $x)); |
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if ($x < ($p + 1.0) / ($p + $q + 2.0)) { |
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return $beta_gam * self::betaFraction($x, $p, $q) / $p; |
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} |
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return 1.0 - ($beta_gam * self::betaFraction(1 - $x, $q, $p) / $q); |
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} |
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// Function cache for logBeta function |
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private static $logBetaCacheP = 0.0; |
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private static $logBetaCacheQ = 0.0; |
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private static $logBetaCacheResult = 0.0; |
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/** |
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* The natural logarithm of the beta function. |
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* |
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* @param mixed $p require p>0 |
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* @param mixed $q require q>0 |
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* |
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* @return float 0 if p<=0, q<=0 or p+q>2.55E305 to avoid errors and over/underflow |
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* |
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* @author Jaco van Kooten |
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*/ |
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private static function logBeta($p, $q) |
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{ |
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if ($p != self::$logBetaCacheP || $q != self::$logBetaCacheQ) { |
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self::$logBetaCacheP = $p; |
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self::$logBetaCacheQ = $q; |
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if (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > self::LOG_GAMMA_X_MAX_VALUE)) { |
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self::$logBetaCacheResult = 0.0; |
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} else { |
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self::$logBetaCacheResult = self::logGamma($p) + self::logGamma($q) - self::logGamma($p + $q); |
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} |
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} |
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return self::$logBetaCacheResult; |
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} |
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/** |
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* Evaluates of continued fraction part of incomplete beta function. |
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* Based on an idea from Numerical Recipes (W.H. Press et al, 1992). |
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* |
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* @author Jaco van Kooten |
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* |
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* @param mixed $x |
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* @param mixed $p |
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* @param mixed $q |
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* |
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* @return float |
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*/ |
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private static function betaFraction($x, $p, $q) |
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{ |
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$c = 1.0; |
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$sum_pq = $p + $q; |
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$p_plus = $p + 1.0; |
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$p_minus = $p - 1.0; |
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$h = 1.0 - $sum_pq * $x / $p_plus; |
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if (abs($h) < self::XMININ) { |
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$h = self::XMININ; |
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} |
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$h = 1.0 / $h; |
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$frac = $h; |
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$m = 1; |
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$delta = 0.0; |
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while ($m <= self::MAX_ITERATIONS && abs($delta - 1.0) > Functions::PRECISION) { |
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$m2 = 2 * $m; |
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// even index for d |
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$d = $m * ($q - $m) * $x / (($p_minus + $m2) * ($p + $m2)); |
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$h = 1.0 + $d * $h; |
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if (abs($h) < self::XMININ) { |
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$h = self::XMININ; |
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} |
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$h = 1.0 / $h; |
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$c = 1.0 + $d / $c; |
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if (abs($c) < self::XMININ) { |
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$c = self::XMININ; |
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} |
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$frac *= $h * $c; |
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// odd index for d |
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$d = -($p + $m) * ($sum_pq + $m) * $x / (($p + $m2) * ($p_plus + $m2)); |
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$h = 1.0 + $d * $h; |
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if (abs($h) < self::XMININ) { |
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$h = self::XMININ; |
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} |
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$h = 1.0 / $h; |
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$c = 1.0 + $d / $c; |
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if (abs($c) < self::XMININ) { |
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$c = self::XMININ; |
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} |
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$delta = $h * $c; |
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$frac *= $delta; |
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++$m; |
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} |
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return $frac; |
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} |
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/** |
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* logGamma function. |
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* |
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* @version 1.1 |
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* |
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* @author Jaco van Kooten |
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* |
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* Original author was Jaco van Kooten. Ported to PHP by Paul Meagher. |
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* |
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* The natural logarithm of the gamma function. <br /> |
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* Based on public domain NETLIB (Fortran) code by W. J. Cody and L. Stoltz <br /> |
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* Applied Mathematics Division <br /> |
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* Argonne National Laboratory <br /> |
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* Argonne, IL 60439 <br /> |
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* <p> |
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* References: |
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* <ol> |
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* <li>W. J. Cody and K. E. Hillstrom, 'Chebyshev Approximations for the Natural |
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* Logarithm of the Gamma Function,' Math. Comp. 21, 1967, pp. 198-203.</li> |
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* <li>K. E. Hillstrom, ANL/AMD Program ANLC366S, DGAMMA/DLGAMA, May, 1969.</li> |
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* <li>Hart, Et. Al., Computer Approximations, Wiley and sons, New York, 1968.</li> |
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* </ol> |
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* </p> |
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* <p> |
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* From the original documentation: |
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* </p> |
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* <p> |
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* This routine calculates the LOG(GAMMA) function for a positive real argument X. |
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* Computation is based on an algorithm outlined in references 1 and 2. |
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* The program uses rational functions that theoretically approximate LOG(GAMMA) |
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* to at least 18 significant decimal digits. The approximation for X > 12 is from |
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* reference 3, while approximations for X < 12.0 are similar to those in reference |
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* 1, but are unpublished. The accuracy achieved depends on the arithmetic system, |
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* the compiler, the intrinsic functions, and proper selection of the |
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* machine-dependent constants. |
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* </p> |
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* <p> |
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* Error returns: <br /> |
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* The program returns the value XINF for X .LE. 0.0 or when overflow would occur. |
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* The computation is believed to be free of underflow and overflow. |
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* </p> |
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* |
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* @return float MAX_VALUE for x < 0.0 or when overflow would occur, i.e. x > 2.55E305 |
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*/ |
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// Function cache for logGamma |
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private static $logGammaCacheResult = 0.0; |
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private static $logGammaCacheX = 0.0; |
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private static function logGamma($x) |
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{ |
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// Log Gamma related constants |
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static $lg_d1 = -0.5772156649015328605195174; |
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static $lg_d2 = 0.4227843350984671393993777; |
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static $lg_d4 = 1.791759469228055000094023; |
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static $lg_p1 = [ |
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4.945235359296727046734888, |
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201.8112620856775083915565, |
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2290.838373831346393026739, |
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11319.67205903380828685045, |
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28557.24635671635335736389, |
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38484.96228443793359990269, |
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26377.48787624195437963534, |
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7225.813979700288197698961, |
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]; |
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static $lg_p2 = [ |
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4.974607845568932035012064, |
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542.4138599891070494101986, |
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15506.93864978364947665077, |
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184793.2904445632425417223, |
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1088204.76946882876749847, |
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3338152.967987029735917223, |
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5106661.678927352456275255, |
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3074109.054850539556250927, |
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]; |
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static $lg_p4 = [ |
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14745.02166059939948905062, |
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2426813.369486704502836312, |
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121475557.4045093227939592, |
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2663432449.630976949898078, |
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29403789566.34553899906876, |
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170266573776.5398868392998, |
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492612579337.743088758812, |
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560625185622.3951465078242, |
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]; |
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static $lg_q1 = [ |
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67.48212550303777196073036, |
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1113.332393857199323513008, |
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7738.757056935398733233834, |
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27639.87074403340708898585, |
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54993.10206226157329794414, |
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61611.22180066002127833352, |
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36351.27591501940507276287, |
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8785.536302431013170870835, |
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]; |
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static $lg_q2 = [ |
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183.0328399370592604055942, |
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7765.049321445005871323047, |
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133190.3827966074194402448, |
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1136705.821321969608938755, |
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5267964.117437946917577538, |
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13467014.54311101692290052, |
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17827365.30353274213975932, |
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9533095.591844353613395747, |
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]; |
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static $lg_q4 = [ |
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2690.530175870899333379843, |
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639388.5654300092398984238, |
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41355999.30241388052042842, |
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1120872109.61614794137657, |
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14886137286.78813811542398, |
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101680358627.2438228077304, |
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341747634550.7377132798597, |
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446315818741.9713286462081, |
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]; |
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static $lg_c = [ |
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-0.001910444077728, |
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8.4171387781295e-4, |
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-5.952379913043012e-4, |
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7.93650793500350248e-4, |
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-0.002777777777777681622553, |
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0.08333333333333333331554247, |
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0.0057083835261, |
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]; |
291
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292
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// Rough estimate of the fourth root of logGamma_xBig |
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4 |
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static $lg_frtbig = 2.25e76; |
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4 |
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static $pnt68 = 0.6796875; |
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296
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4 |
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if ($x == self::$logGammaCacheX) { |
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return self::$logGammaCacheResult; |
298
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} |
299
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4 |
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$y = $x; |
300
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4 |
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if ($y > 0.0 && $y <= self::LOG_GAMMA_X_MAX_VALUE) { |
301
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4 |
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if ($y <= self::EPS) { |
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$res = -log($y); |
303
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4 |
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} elseif ($y <= 1.5) { |
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// --------------------- |
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// EPS .LT. X .LE. 1.5 |
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// --------------------- |
307
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if ($y < $pnt68) { |
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$corr = -log($y); |
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$xm1 = $y; |
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} else { |
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$corr = 0.0; |
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$xm1 = $y - 1.0; |
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} |
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if ($y <= 0.5 || $y >= $pnt68) { |
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$xden = 1.0; |
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$xnum = 0.0; |
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for ($i = 0; $i < 8; ++$i) { |
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$xnum = $xnum * $xm1 + $lg_p1[$i]; |
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$xden = $xden * $xm1 + $lg_q1[$i]; |
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} |
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$res = $corr + $xm1 * ($lg_d1 + $xm1 * ($xnum / $xden)); |
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} else { |
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$xm2 = $y - 1.0; |
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$xden = 1.0; |
325
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$xnum = 0.0; |
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for ($i = 0; $i < 8; ++$i) { |
327
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$xnum = $xnum * $xm2 + $lg_p2[$i]; |
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|
|
$xden = $xden * $xm2 + $lg_q2[$i]; |
329
|
|
|
} |
330
|
|
|
$res = $corr + $xm2 * ($lg_d2 + $xm2 * ($xnum / $xden)); |
331
|
|
|
} |
332
|
4 |
|
} elseif ($y <= 4.0) { |
333
|
|
|
// --------------------- |
334
|
|
|
// 1.5 .LT. X .LE. 4.0 |
335
|
|
|
// --------------------- |
336
|
|
|
$xm2 = $y - 2.0; |
337
|
|
|
$xden = 1.0; |
338
|
|
|
$xnum = 0.0; |
339
|
|
|
for ($i = 0; $i < 8; ++$i) { |
340
|
|
|
$xnum = $xnum * $xm2 + $lg_p2[$i]; |
341
|
|
|
$xden = $xden * $xm2 + $lg_q2[$i]; |
342
|
|
|
} |
343
|
|
|
$res = $xm2 * ($lg_d2 + $xm2 * ($xnum / $xden)); |
344
|
4 |
|
} elseif ($y <= 12.0) { |
345
|
|
|
// ---------------------- |
346
|
|
|
// 4.0 .LT. X .LE. 12.0 |
347
|
|
|
// ---------------------- |
348
|
4 |
|
$xm4 = $y - 4.0; |
349
|
4 |
|
$xden = -1.0; |
350
|
4 |
|
$xnum = 0.0; |
351
|
4 |
|
for ($i = 0; $i < 8; ++$i) { |
352
|
4 |
|
$xnum = $xnum * $xm4 + $lg_p4[$i]; |
353
|
4 |
|
$xden = $xden * $xm4 + $lg_q4[$i]; |
354
|
|
|
} |
355
|
4 |
|
$res = $lg_d4 + $xm4 * ($xnum / $xden); |
356
|
|
|
} else { |
357
|
|
|
// --------------------------------- |
358
|
|
|
// Evaluate for argument .GE. 12.0 |
359
|
|
|
// --------------------------------- |
360
|
4 |
|
$res = 0.0; |
361
|
4 |
|
if ($y <= $lg_frtbig) { |
362
|
4 |
|
$res = $lg_c[6]; |
363
|
4 |
|
$ysq = $y * $y; |
364
|
4 |
|
for ($i = 0; $i < 6; ++$i) { |
365
|
4 |
|
$res = $res / $ysq + $lg_c[$i]; |
366
|
|
|
} |
367
|
4 |
|
$res /= $y; |
368
|
4 |
|
$corr = log($y); |
369
|
4 |
|
$res = $res + log(self::SQRT2PI) - 0.5 * $corr; |
370
|
4 |
|
$res += $y * ($corr - 1.0); |
371
|
|
|
} |
372
|
|
|
} |
373
|
|
|
} else { |
374
|
|
|
// -------------------------- |
375
|
|
|
// Return for bad arguments |
376
|
|
|
// -------------------------- |
377
|
|
|
$res = self::MAX_VALUE; |
378
|
|
|
} |
379
|
|
|
// ------------------------------ |
380
|
|
|
// Final adjustments and return |
381
|
|
|
// ------------------------------ |
382
|
4 |
|
self::$logGammaCacheX = $x; |
383
|
4 |
|
self::$logGammaCacheResult = $res; |
384
|
|
|
|
385
|
4 |
|
return $res; |
386
|
|
|
} |
387
|
|
|
|
388
|
|
|
// |
389
|
|
|
// Private implementation of the incomplete Gamma function |
390
|
|
|
// |
391
|
|
|
private static function incompleteGamma($a, $x) |
392
|
|
|
{ |
393
|
|
|
static $max = 32; |
394
|
|
|
$summer = 0; |
395
|
|
|
for ($n = 0; $n <= $max; ++$n) { |
396
|
|
|
$divisor = $a; |
397
|
|
|
for ($i = 1; $i <= $n; ++$i) { |
398
|
|
|
$divisor *= ($a + $i); |
399
|
|
|
} |
400
|
|
|
$summer += (pow($x, $n) / $divisor); |
401
|
|
|
} |
402
|
|
|
|
403
|
|
|
return pow($x, $a) * exp(0 - $x) * $summer; |
404
|
|
|
} |
405
|
|
|
|
406
|
|
|
// |
407
|
|
|
// Private implementation of the Gamma function |
408
|
|
|
// |
409
|
|
|
private static function gamma($data) |
410
|
|
|
{ |
411
|
|
|
if ($data == 0.0) { |
412
|
|
|
return 0; |
413
|
|
|
} |
414
|
|
|
|
415
|
|
|
static $p0 = 1.000000000190015; |
416
|
|
|
static $p = [ |
417
|
|
|
1 => 76.18009172947146, |
418
|
|
|
2 => -86.50532032941677, |
419
|
|
|
3 => 24.01409824083091, |
420
|
|
|
4 => -1.231739572450155, |
421
|
|
|
5 => 1.208650973866179e-3, |
422
|
|
|
6 => -5.395239384953e-6, |
423
|
|
|
]; |
424
|
|
|
|
425
|
|
|
$y = $x = $data; |
426
|
|
|
$tmp = $x + 5.5; |
427
|
|
|
$tmp -= ($x + 0.5) * log($tmp); |
428
|
|
|
|
429
|
|
|
$summer = $p0; |
430
|
|
|
for ($j = 1; $j <= 6; ++$j) { |
431
|
|
|
$summer += ($p[$j] / ++$y); |
432
|
|
|
} |
433
|
|
|
|
434
|
|
|
return exp(0 - $tmp + log(self::SQRT2PI * $summer / $x)); |
435
|
|
|
} |
436
|
|
|
|
437
|
|
|
/* |
438
|
|
|
* inverse_ncdf.php |
439
|
|
|
* ------------------- |
440
|
|
|
* begin : Friday, January 16, 2004 |
441
|
|
|
* copyright : (C) 2004 Michael Nickerson |
442
|
|
|
* email : [email protected] |
443
|
|
|
* |
444
|
|
|
*/ |
445
|
|
|
private static function inverseNcdf($p) |
446
|
|
|
{ |
447
|
|
|
// Inverse ncdf approximation by Peter J. Acklam, implementation adapted to |
448
|
|
|
// PHP by Michael Nickerson, using Dr. Thomas Ziegler's C implementation as |
449
|
|
|
// a guide. http://home.online.no/~pjacklam/notes/invnorm/index.html |
450
|
|
|
// I have not checked the accuracy of this implementation. Be aware that PHP |
451
|
|
|
// will truncate the coeficcients to 14 digits. |
452
|
|
|
|
453
|
|
|
// You have permission to use and distribute this function freely for |
454
|
|
|
// whatever purpose you want, but please show common courtesy and give credit |
455
|
|
|
// where credit is due. |
456
|
|
|
|
457
|
|
|
// Input paramater is $p - probability - where 0 < p < 1. |
458
|
|
|
|
459
|
|
|
// Coefficients in rational approximations |
460
|
|
|
static $a = [ |
461
|
|
|
1 => -3.969683028665376e+01, |
462
|
|
|
2 => 2.209460984245205e+02, |
463
|
|
|
3 => -2.759285104469687e+02, |
464
|
|
|
4 => 1.383577518672690e+02, |
465
|
|
|
5 => -3.066479806614716e+01, |
466
|
|
|
6 => 2.506628277459239e+00, |
467
|
|
|
]; |
468
|
|
|
|
469
|
|
|
static $b = [ |
470
|
|
|
1 => -5.447609879822406e+01, |
471
|
|
|
2 => 1.615858368580409e+02, |
472
|
|
|
3 => -1.556989798598866e+02, |
473
|
|
|
4 => 6.680131188771972e+01, |
474
|
|
|
5 => -1.328068155288572e+01, |
475
|
|
|
]; |
476
|
|
|
|
477
|
|
|
static $c = [ |
478
|
|
|
1 => -7.784894002430293e-03, |
479
|
|
|
2 => -3.223964580411365e-01, |
480
|
|
|
3 => -2.400758277161838e+00, |
481
|
|
|
4 => -2.549732539343734e+00, |
482
|
|
|
5 => 4.374664141464968e+00, |
483
|
|
|
6 => 2.938163982698783e+00, |
484
|
|
|
]; |
485
|
|
|
|
486
|
|
|
static $d = [ |
487
|
|
|
1 => 7.784695709041462e-03, |
488
|
|
|
2 => 3.224671290700398e-01, |
489
|
|
|
3 => 2.445134137142996e+00, |
490
|
|
|
4 => 3.754408661907416e+00, |
491
|
|
|
]; |
492
|
|
|
|
493
|
|
|
// Define lower and upper region break-points. |
494
|
|
|
$p_low = 0.02425; //Use lower region approx. below this |
495
|
|
|
$p_high = 1 - $p_low; //Use upper region approx. above this |
496
|
|
|
|
497
|
|
|
if (0 < $p && $p < $p_low) { |
498
|
|
|
// Rational approximation for lower region. |
499
|
|
|
$q = sqrt(-2 * log($p)); |
500
|
|
|
|
501
|
|
|
return ((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6]) / |
502
|
|
|
(((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1); |
503
|
|
|
} elseif ($p_low <= $p && $p <= $p_high) { |
504
|
|
|
// Rational approximation for central region. |
505
|
|
|
$q = $p - 0.5; |
506
|
|
|
$r = $q * $q; |
507
|
|
|
|
508
|
|
|
return ((((($a[1] * $r + $a[2]) * $r + $a[3]) * $r + $a[4]) * $r + $a[5]) * $r + $a[6]) * $q / |
509
|
|
|
((((($b[1] * $r + $b[2]) * $r + $b[3]) * $r + $b[4]) * $r + $b[5]) * $r + 1); |
510
|
|
|
} elseif ($p_high < $p && $p < 1) { |
511
|
|
|
// Rational approximation for upper region. |
512
|
|
|
$q = sqrt(-2 * log(1 - $p)); |
513
|
|
|
|
514
|
|
|
return -((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6]) / |
515
|
|
|
(((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1); |
516
|
|
|
} |
517
|
|
|
// If 0 < p < 1, return a null value |
518
|
|
|
return Functions::NULL(); |
519
|
|
|
} |
520
|
|
|
|
521
|
|
|
/** |
522
|
|
|
* AVEDEV. |
523
|
|
|
* |
524
|
|
|
* Returns the average of the absolute deviations of data points from their mean. |
525
|
|
|
* AVEDEV is a measure of the variability in a data set. |
526
|
|
|
* |
527
|
|
|
* Excel Function: |
528
|
|
|
* AVEDEV(value1[,value2[, ...]]) |
529
|
|
|
* |
530
|
|
|
* @category Statistical Functions |
531
|
|
|
* |
532
|
|
|
* @param mixed ...$args Data values |
533
|
|
|
* |
534
|
|
|
* @return float|string |
535
|
|
|
*/ |
536
|
4 |
|
public static function AVEDEV(...$args) |
537
|
|
|
{ |
538
|
4 |
|
$aArgs = Functions::flattenArrayIndexed($args); |
539
|
|
|
|
540
|
|
|
// Return value |
541
|
4 |
|
$returnValue = null; |
542
|
|
|
|
543
|
4 |
|
$aMean = self::AVERAGE($aArgs); |
544
|
4 |
|
if ($aMean != Functions::DIV0()) { |
545
|
4 |
|
$aCount = 0; |
546
|
4 |
|
foreach ($aArgs as $k => $arg) { |
547
|
4 |
|
if ((is_bool($arg)) && |
548
|
4 |
|
((!Functions::isCellValue($k)) || (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE))) { |
549
|
|
|
$arg = (int) $arg; |
550
|
|
|
} |
551
|
|
|
// Is it a numeric value? |
552
|
4 |
|
if ((is_numeric($arg)) && (!is_string($arg))) { |
553
|
4 |
|
if ($returnValue === null) { |
554
|
4 |
|
$returnValue = abs($arg - $aMean); |
555
|
|
|
} else { |
556
|
4 |
|
$returnValue += abs($arg - $aMean); |
557
|
|
|
} |
558
|
4 |
|
++$aCount; |
559
|
|
|
} |
560
|
|
|
} |
561
|
|
|
|
562
|
|
|
// Return |
563
|
4 |
|
if ($aCount == 0) { |
564
|
|
|
return Functions::DIV0(); |
565
|
|
|
} |
566
|
|
|
|
567
|
4 |
|
return $returnValue / $aCount; |
568
|
|
|
} |
569
|
|
|
|
570
|
|
|
return Functions::NAN(); |
571
|
|
|
} |
572
|
|
|
|
573
|
|
|
/** |
574
|
|
|
* AVERAGE. |
575
|
|
|
* |
576
|
|
|
* Returns the average (arithmetic mean) of the arguments |
577
|
|
|
* |
578
|
|
|
* Excel Function: |
579
|
|
|
* AVERAGE(value1[,value2[, ...]]) |
580
|
|
|
* |
581
|
|
|
* @category Statistical Functions |
582
|
|
|
* |
583
|
|
|
* @param mixed ...$args Data values |
584
|
|
|
* |
585
|
|
|
* @return float|string |
586
|
|
|
*/ |
587
|
21 |
|
public static function AVERAGE(...$args) |
588
|
|
|
{ |
589
|
21 |
|
$returnValue = $aCount = 0; |
590
|
|
|
|
591
|
|
|
// Loop through arguments |
592
|
21 |
|
foreach (Functions::flattenArrayIndexed($args) as $k => $arg) { |
593
|
21 |
|
if ((is_bool($arg)) && |
594
|
21 |
|
((!Functions::isCellValue($k)) || (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE))) { |
595
|
|
|
$arg = (int) $arg; |
596
|
|
|
} |
597
|
|
|
// Is it a numeric value? |
598
|
21 |
|
if ((is_numeric($arg)) && (!is_string($arg))) { |
599
|
21 |
|
if ($returnValue === null) { |
600
|
|
|
$returnValue = $arg; |
601
|
|
|
} else { |
602
|
21 |
|
$returnValue += $arg; |
603
|
|
|
} |
604
|
21 |
|
++$aCount; |
605
|
|
|
} |
606
|
|
|
} |
607
|
|
|
|
608
|
|
|
// Return |
609
|
21 |
|
if ($aCount > 0) { |
610
|
21 |
|
return $returnValue / $aCount; |
611
|
|
|
} |
612
|
|
|
|
613
|
|
|
return Functions::DIV0(); |
614
|
|
|
} |
615
|
|
|
|
616
|
|
|
/** |
617
|
|
|
* AVERAGEA. |
618
|
|
|
* |
619
|
|
|
* Returns the average of its arguments, including numbers, text, and logical values |
620
|
|
|
* |
621
|
|
|
* Excel Function: |
622
|
|
|
* AVERAGEA(value1[,value2[, ...]]) |
623
|
|
|
* |
624
|
|
|
* @category Statistical Functions |
625
|
|
|
* |
626
|
|
|
* @param mixed ...$args Data values |
627
|
|
|
* |
628
|
|
|
* @return float|string |
629
|
|
|
*/ |
630
|
6 |
|
public static function AVERAGEA(...$args) |
631
|
|
|
{ |
632
|
6 |
|
$returnValue = null; |
633
|
|
|
|
634
|
6 |
|
$aCount = 0; |
635
|
|
|
// Loop through arguments |
636
|
6 |
|
foreach (Functions::flattenArrayIndexed($args) as $k => $arg) { |
637
|
6 |
|
if ((is_bool($arg)) && |
638
|
6 |
|
(!Functions::isMatrixValue($k))) { |
639
|
|
|
} else { |
640
|
6 |
|
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) && ($arg != '')))) { |
641
|
6 |
|
if (is_bool($arg)) { |
642
|
3 |
|
$arg = (int) $arg; |
643
|
5 |
|
} elseif (is_string($arg)) { |
644
|
2 |
|
$arg = 0; |
645
|
|
|
} |
646
|
6 |
|
if ($returnValue === null) { |
647
|
6 |
|
$returnValue = $arg; |
648
|
|
|
} else { |
649
|
6 |
|
$returnValue += $arg; |
650
|
|
|
} |
651
|
6 |
|
++$aCount; |
652
|
|
|
} |
653
|
|
|
} |
654
|
|
|
} |
655
|
|
|
|
656
|
6 |
|
if ($aCount > 0) { |
657
|
6 |
|
return $returnValue / $aCount; |
658
|
|
|
} |
659
|
|
|
|
660
|
|
|
return Functions::DIV0(); |
661
|
|
|
} |
662
|
|
|
|
663
|
|
|
/** |
664
|
|
|
* AVERAGEIF. |
665
|
|
|
* |
666
|
|
|
* Returns the average value from a range of cells that contain numbers within the list of arguments |
667
|
|
|
* |
668
|
|
|
* Excel Function: |
669
|
|
|
* AVERAGEIF(value1[,value2[, ...]],condition) |
670
|
|
|
* |
671
|
|
|
* @category Mathematical and Trigonometric Functions |
672
|
|
|
* |
673
|
|
|
* @param mixed $aArgs Data values |
674
|
|
|
* @param string $condition the criteria that defines which cells will be checked |
675
|
|
|
* @param mixed[] $averageArgs Data values |
676
|
|
|
* |
677
|
|
|
* @return float|string |
678
|
|
|
*/ |
679
|
8 |
|
public static function AVERAGEIF($aArgs, $condition, $averageArgs = []) |
680
|
|
|
{ |
681
|
8 |
|
$returnValue = 0; |
682
|
|
|
|
683
|
8 |
|
$aArgs = Functions::flattenArray($aArgs); |
684
|
8 |
|
$averageArgs = Functions::flattenArray($averageArgs); |
685
|
8 |
|
if (empty($averageArgs)) { |
686
|
4 |
|
$averageArgs = $aArgs; |
687
|
|
|
} |
688
|
8 |
|
$condition = Functions::ifCondition($condition); |
689
|
8 |
|
$conditionIsNumeric = strpos($condition, '"') === false; |
690
|
|
|
|
691
|
|
|
// Loop through arguments |
692
|
8 |
|
$aCount = 0; |
693
|
8 |
|
foreach ($aArgs as $key => $arg) { |
694
|
8 |
|
if (!is_numeric($arg)) { |
695
|
|
|
if ($conditionIsNumeric) { |
696
|
|
|
continue; |
697
|
|
|
} |
698
|
|
|
$arg = Calculation::wrapResult(strtoupper($arg)); |
699
|
8 |
|
} elseif (!$conditionIsNumeric) { |
700
|
|
|
continue; |
701
|
|
|
} |
702
|
8 |
|
$testCondition = '=' . $arg . $condition; |
703
|
8 |
|
if (Calculation::getInstance()->_calculateFormulaValue($testCondition)) { |
704
|
7 |
|
$returnValue += $averageArgs[$key]; |
705
|
7 |
|
++$aCount; |
706
|
|
|
} |
707
|
|
|
} |
708
|
|
|
|
709
|
8 |
|
if ($aCount > 0) { |
710
|
7 |
|
return $returnValue / $aCount; |
711
|
|
|
} |
712
|
|
|
|
713
|
1 |
|
return Functions::DIV0(); |
714
|
|
|
} |
715
|
|
|
|
716
|
|
|
/** |
717
|
|
|
* BETADIST. |
718
|
|
|
* |
719
|
|
|
* Returns the beta distribution. |
720
|
|
|
* |
721
|
|
|
* @param float $value Value at which you want to evaluate the distribution |
722
|
|
|
* @param float $alpha Parameter to the distribution |
723
|
|
|
* @param float $beta Parameter to the distribution |
724
|
|
|
* @param mixed $rMin |
725
|
|
|
* @param mixed $rMax |
726
|
|
|
* |
727
|
|
|
* @return float|string |
728
|
|
|
*/ |
729
|
4 |
|
public static function BETADIST($value, $alpha, $beta, $rMin = 0, $rMax = 1) |
730
|
|
|
{ |
731
|
4 |
|
$value = Functions::flattenSingleValue($value); |
732
|
4 |
|
$alpha = Functions::flattenSingleValue($alpha); |
733
|
4 |
|
$beta = Functions::flattenSingleValue($beta); |
734
|
4 |
|
$rMin = Functions::flattenSingleValue($rMin); |
735
|
4 |
|
$rMax = Functions::flattenSingleValue($rMax); |
736
|
|
|
|
737
|
4 |
|
if ((is_numeric($value)) && (is_numeric($alpha)) && (is_numeric($beta)) && (is_numeric($rMin)) && (is_numeric($rMax))) { |
738
|
4 |
|
if (($value < $rMin) || ($value > $rMax) || ($alpha <= 0) || ($beta <= 0) || ($rMin == $rMax)) { |
739
|
|
|
return Functions::NAN(); |
740
|
|
|
} |
741
|
4 |
|
if ($rMin > $rMax) { |
742
|
|
|
$tmp = $rMin; |
743
|
|
|
$rMin = $rMax; |
744
|
|
|
$rMax = $tmp; |
745
|
|
|
} |
746
|
4 |
|
$value -= $rMin; |
747
|
4 |
|
$value /= ($rMax - $rMin); |
748
|
|
|
|
749
|
4 |
|
return self::incompleteBeta($value, $alpha, $beta); |
750
|
|
|
} |
751
|
|
|
|
752
|
|
|
return Functions::VALUE(); |
753
|
|
|
} |
754
|
|
|
|
755
|
|
|
/** |
756
|
|
|
* BETAINV. |
757
|
|
|
* |
758
|
|
|
* Returns the inverse of the beta distribution. |
759
|
|
|
* |
760
|
|
|
* @param float $probability Probability at which you want to evaluate the distribution |
761
|
|
|
* @param float $alpha Parameter to the distribution |
762
|
|
|
* @param float $beta Parameter to the distribution |
763
|
|
|
* @param float $rMin Minimum value |
764
|
|
|
* @param float $rMax Maximum value |
765
|
|
|
* |
766
|
|
|
* @return float|string |
767
|
|
|
*/ |
768
|
2 |
|
public static function BETAINV($probability, $alpha, $beta, $rMin = 0, $rMax = 1) |
769
|
|
|
{ |
770
|
2 |
|
$probability = Functions::flattenSingleValue($probability); |
771
|
2 |
|
$alpha = Functions::flattenSingleValue($alpha); |
772
|
2 |
|
$beta = Functions::flattenSingleValue($beta); |
773
|
2 |
|
$rMin = Functions::flattenSingleValue($rMin); |
774
|
2 |
|
$rMax = Functions::flattenSingleValue($rMax); |
775
|
|
|
|
776
|
2 |
|
if ((is_numeric($probability)) && (is_numeric($alpha)) && (is_numeric($beta)) && (is_numeric($rMin)) && (is_numeric($rMax))) { |
777
|
2 |
|
if (($alpha <= 0) || ($beta <= 0) || ($rMin == $rMax) || ($probability <= 0) || ($probability > 1)) { |
778
|
|
|
return Functions::NAN(); |
779
|
|
|
} |
780
|
2 |
|
if ($rMin > $rMax) { |
781
|
|
|
$tmp = $rMin; |
782
|
|
|
$rMin = $rMax; |
783
|
|
|
$rMax = $tmp; |
784
|
|
|
} |
785
|
2 |
|
$a = 0; |
786
|
2 |
|
$b = 2; |
787
|
|
|
|
788
|
2 |
|
$i = 0; |
789
|
2 |
|
while ((($b - $a) > Functions::PRECISION) && ($i++ < self::MAX_ITERATIONS)) { |
790
|
2 |
|
$guess = ($a + $b) / 2; |
791
|
2 |
|
$result = self::BETADIST($guess, $alpha, $beta); |
792
|
2 |
|
if (($result == $probability) || ($result == 0)) { |
793
|
|
|
$b = $a; |
794
|
2 |
|
} elseif ($result > $probability) { |
795
|
2 |
|
$b = $guess; |
796
|
|
|
} else { |
797
|
2 |
|
$a = $guess; |
798
|
|
|
} |
799
|
|
|
} |
800
|
2 |
|
if ($i == self::MAX_ITERATIONS) { |
801
|
|
|
return Functions::NA(); |
802
|
|
|
} |
803
|
|
|
|
804
|
2 |
|
return round($rMin + $guess * ($rMax - $rMin), 12); |
|
|
|
|
805
|
|
|
} |
806
|
|
|
|
807
|
|
|
return Functions::VALUE(); |
808
|
|
|
} |
809
|
|
|
|
810
|
|
|
/** |
811
|
|
|
* BINOMDIST. |
812
|
|
|
* |
813
|
|
|
* Returns the individual term binomial distribution probability. Use BINOMDIST in problems with |
814
|
|
|
* a fixed number of tests or trials, when the outcomes of any trial are only success or failure, |
815
|
|
|
* when trials are independent, and when the probability of success is constant throughout the |
816
|
|
|
* experiment. For example, BINOMDIST can calculate the probability that two of the next three |
817
|
|
|
* babies born are male. |
818
|
|
|
* |
819
|
|
|
* @param float $value Number of successes in trials |
820
|
|
|
* @param float $trials Number of trials |
821
|
|
|
* @param float $probability Probability of success on each trial |
822
|
|
|
* @param bool $cumulative |
823
|
|
|
* |
824
|
|
|
* @return float |
825
|
|
|
* |
826
|
|
|
* @todo Cumulative distribution function |
827
|
|
|
*/ |
828
|
|
|
public static function BINOMDIST($value, $trials, $probability, $cumulative) |
829
|
|
|
{ |
830
|
|
|
$value = floor(Functions::flattenSingleValue($value)); |
831
|
|
|
$trials = floor(Functions::flattenSingleValue($trials)); |
832
|
|
|
$probability = Functions::flattenSingleValue($probability); |
833
|
|
|
|
834
|
|
|
if ((is_numeric($value)) && (is_numeric($trials)) && (is_numeric($probability))) { |
|
|
|
|
835
|
|
|
if (($value < 0) || ($value > $trials)) { |
836
|
|
|
return Functions::NAN(); |
|
|
|
|
837
|
|
|
} |
838
|
|
|
if (($probability < 0) || ($probability > 1)) { |
839
|
|
|
return Functions::NAN(); |
|
|
|
|
840
|
|
|
} |
841
|
|
|
if ((is_numeric($cumulative)) || (is_bool($cumulative))) { |
|
|
|
|
842
|
|
|
if ($cumulative) { |
843
|
|
|
$summer = 0; |
844
|
|
|
for ($i = 0; $i <= $value; ++$i) { |
845
|
|
|
$summer += MathTrig::COMBIN($trials, $i) * pow($probability, $i) * pow(1 - $probability, $trials - $i); |
|
|
|
|
846
|
|
|
} |
847
|
|
|
|
848
|
|
|
return $summer; |
849
|
|
|
} |
850
|
|
|
|
851
|
|
|
return MathTrig::COMBIN($trials, $value) * pow($probability, $value) * pow(1 - $probability, $trials - $value); |
|
|
|
|
852
|
|
|
} |
853
|
|
|
} |
854
|
|
|
|
855
|
|
|
return Functions::VALUE(); |
|
|
|
|
856
|
|
|
} |
857
|
|
|
|
858
|
|
|
/** |
859
|
|
|
* CHIDIST. |
860
|
|
|
* |
861
|
|
|
* Returns the one-tailed probability of the chi-squared distribution. |
862
|
|
|
* |
863
|
|
|
* @param float $value Value for the function |
864
|
|
|
* @param float $degrees degrees of freedom |
865
|
|
|
* |
866
|
|
|
* @return float |
867
|
|
|
*/ |
868
|
|
|
public static function CHIDIST($value, $degrees) |
869
|
|
|
{ |
870
|
|
|
$value = Functions::flattenSingleValue($value); |
871
|
|
|
$degrees = floor(Functions::flattenSingleValue($degrees)); |
872
|
|
|
|
873
|
|
|
if ((is_numeric($value)) && (is_numeric($degrees))) { |
874
|
|
|
if ($degrees < 1) { |
875
|
|
|
return Functions::NAN(); |
|
|
|
|
876
|
|
|
} |
877
|
|
|
if ($value < 0) { |
878
|
|
|
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_GNUMERIC) { |
879
|
|
|
return 1; |
880
|
|
|
} |
881
|
|
|
|
882
|
|
|
return Functions::NAN(); |
|
|
|
|
883
|
|
|
} |
884
|
|
|
|
885
|
|
|
return 1 - (self::incompleteGamma($degrees / 2, $value / 2) / self::gamma($degrees / 2)); |
886
|
|
|
} |
887
|
|
|
|
888
|
|
|
return Functions::VALUE(); |
|
|
|
|
889
|
|
|
} |
890
|
|
|
|
891
|
|
|
/** |
892
|
|
|
* CHIINV. |
893
|
|
|
* |
894
|
|
|
* Returns the one-tailed probability of the chi-squared distribution. |
895
|
|
|
* |
896
|
|
|
* @param float $probability Probability for the function |
897
|
|
|
* @param float $degrees degrees of freedom |
898
|
|
|
* |
899
|
|
|
* @return float |
900
|
|
|
*/ |
901
|
|
|
public static function CHIINV($probability, $degrees) |
902
|
|
|
{ |
903
|
|
|
$probability = Functions::flattenSingleValue($probability); |
904
|
|
|
$degrees = floor(Functions::flattenSingleValue($degrees)); |
905
|
|
|
|
906
|
|
|
if ((is_numeric($probability)) && (is_numeric($degrees))) { |
907
|
|
|
$xLo = 100; |
908
|
|
|
$xHi = 0; |
909
|
|
|
|
910
|
|
|
$x = $xNew = 1; |
911
|
|
|
$dx = 1; |
912
|
|
|
$i = 0; |
913
|
|
|
|
914
|
|
|
while ((abs($dx) > Functions::PRECISION) && ($i++ < self::MAX_ITERATIONS)) { |
915
|
|
|
// Apply Newton-Raphson step |
916
|
|
|
$result = self::CHIDIST($x, $degrees); |
917
|
|
|
$error = $result - $probability; |
918
|
|
|
if ($error == 0.0) { |
919
|
|
|
$dx = 0; |
920
|
|
|
} elseif ($error < 0.0) { |
921
|
|
|
$xLo = $x; |
922
|
|
|
} else { |
923
|
|
|
$xHi = $x; |
924
|
|
|
} |
925
|
|
|
// Avoid division by zero |
926
|
|
|
if ($result != 0.0) { |
927
|
|
|
$dx = $error / $result; |
928
|
|
|
$xNew = $x - $dx; |
929
|
|
|
} |
930
|
|
|
// If the NR fails to converge (which for example may be the |
931
|
|
|
// case if the initial guess is too rough) we apply a bisection |
932
|
|
|
// step to determine a more narrow interval around the root. |
933
|
|
|
if (($xNew < $xLo) || ($xNew > $xHi) || ($result == 0.0)) { |
934
|
|
|
$xNew = ($xLo + $xHi) / 2; |
935
|
|
|
$dx = $xNew - $x; |
936
|
|
|
} |
937
|
|
|
$x = $xNew; |
938
|
|
|
} |
939
|
|
|
if ($i == self::MAX_ITERATIONS) { |
940
|
|
|
return Functions::NA(); |
|
|
|
|
941
|
|
|
} |
942
|
|
|
|
943
|
|
|
return round($x, 12); |
944
|
|
|
} |
945
|
|
|
|
946
|
|
|
return Functions::VALUE(); |
|
|
|
|
947
|
|
|
} |
948
|
|
|
|
949
|
|
|
/** |
950
|
|
|
* CONFIDENCE. |
951
|
|
|
* |
952
|
|
|
* Returns the confidence interval for a population mean |
953
|
|
|
* |
954
|
|
|
* @param float $alpha |
955
|
|
|
* @param float $stdDev Standard Deviation |
956
|
|
|
* @param float $size |
957
|
|
|
* |
958
|
|
|
* @return float |
959
|
|
|
*/ |
960
|
|
|
public static function CONFIDENCE($alpha, $stdDev, $size) |
961
|
|
|
{ |
962
|
|
|
$alpha = Functions::flattenSingleValue($alpha); |
963
|
|
|
$stdDev = Functions::flattenSingleValue($stdDev); |
964
|
|
|
$size = floor(Functions::flattenSingleValue($size)); |
965
|
|
|
|
966
|
|
|
if ((is_numeric($alpha)) && (is_numeric($stdDev)) && (is_numeric($size))) { |
967
|
|
|
if (($alpha <= 0) || ($alpha >= 1)) { |
968
|
|
|
return Functions::NAN(); |
|
|
|
|
969
|
|
|
} |
970
|
|
|
if (($stdDev <= 0) || ($size < 1)) { |
971
|
|
|
return Functions::NAN(); |
|
|
|
|
972
|
|
|
} |
973
|
|
|
|
974
|
|
|
return self::NORMSINV(1 - $alpha / 2) * $stdDev / sqrt($size); |
975
|
|
|
} |
976
|
|
|
|
977
|
|
|
return Functions::VALUE(); |
|
|
|
|
978
|
|
|
} |
979
|
|
|
|
980
|
|
|
/** |
981
|
|
|
* CORREL. |
982
|
|
|
* |
983
|
|
|
* Returns covariance, the average of the products of deviations for each data point pair. |
984
|
|
|
* |
985
|
|
|
* @param mixed $yValues array of mixed Data Series Y |
986
|
|
|
* @param null|mixed $xValues array of mixed Data Series X |
987
|
|
|
* |
988
|
|
|
* @return float |
989
|
|
|
*/ |
990
|
|
|
public static function CORREL($yValues, $xValues = null) |
991
|
|
|
{ |
992
|
|
|
if (($xValues === null) || (!is_array($yValues)) || (!is_array($xValues))) { |
993
|
|
|
return Functions::VALUE(); |
|
|
|
|
994
|
|
|
} |
995
|
|
|
if (!self::checkTrendArrays($yValues, $xValues)) { |
996
|
|
|
return Functions::VALUE(); |
|
|
|
|
997
|
|
|
} |
998
|
|
|
$yValueCount = count($yValues); |
999
|
|
|
$xValueCount = count($xValues); |
1000
|
|
|
|
1001
|
|
|
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) { |
1002
|
|
|
return Functions::NA(); |
|
|
|
|
1003
|
|
|
} elseif ($yValueCount == 1) { |
1004
|
|
|
return Functions::DIV0(); |
|
|
|
|
1005
|
|
|
} |
1006
|
|
|
|
1007
|
|
|
$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues); |
1008
|
|
|
|
1009
|
|
|
return $bestFitLinear->getCorrelation(); |
1010
|
|
|
} |
1011
|
|
|
|
1012
|
|
|
/** |
1013
|
|
|
* COUNT. |
1014
|
|
|
* |
1015
|
|
|
* Counts the number of cells that contain numbers within the list of arguments |
1016
|
|
|
* |
1017
|
|
|
* Excel Function: |
1018
|
|
|
* COUNT(value1[,value2[, ...]]) |
1019
|
|
|
* |
1020
|
|
|
* @category Statistical Functions |
1021
|
|
|
* |
1022
|
|
|
* @param mixed ...$args Data values |
1023
|
|
|
* |
1024
|
|
|
* @return int |
1025
|
|
|
*/ |
1026
|
5 |
|
public static function COUNT(...$args) |
1027
|
|
|
{ |
1028
|
5 |
|
$returnValue = 0; |
1029
|
|
|
|
1030
|
|
|
// Loop through arguments |
1031
|
5 |
|
$aArgs = Functions::flattenArrayIndexed($args); |
1032
|
5 |
|
foreach ($aArgs as $k => $arg) { |
1033
|
5 |
|
if ((is_bool($arg)) && |
1034
|
5 |
|
((!Functions::isCellValue($k)) || (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE))) { |
1035
|
|
|
$arg = (int) $arg; |
1036
|
|
|
} |
1037
|
|
|
// Is it a numeric value? |
1038
|
5 |
|
if ((is_numeric($arg)) && (!is_string($arg))) { |
1039
|
5 |
|
++$returnValue; |
1040
|
|
|
} |
1041
|
|
|
} |
1042
|
|
|
|
1043
|
5 |
|
return $returnValue; |
1044
|
|
|
} |
1045
|
|
|
|
1046
|
|
|
/** |
1047
|
|
|
* COUNTA. |
1048
|
|
|
* |
1049
|
|
|
* Counts the number of cells that are not empty within the list of arguments |
1050
|
|
|
* |
1051
|
|
|
* Excel Function: |
1052
|
|
|
* COUNTA(value1[,value2[, ...]]) |
1053
|
|
|
* |
1054
|
|
|
* @category Statistical Functions |
1055
|
|
|
* |
1056
|
|
|
* @param mixed ...$args Data values |
1057
|
|
|
* |
1058
|
|
|
* @return int |
1059
|
|
|
*/ |
1060
|
3 |
|
public static function COUNTA(...$args) |
1061
|
|
|
{ |
1062
|
3 |
|
$returnValue = 0; |
1063
|
|
|
|
1064
|
|
|
// Loop through arguments |
1065
|
3 |
|
$aArgs = Functions::flattenArray($args); |
1066
|
3 |
|
foreach ($aArgs as $arg) { |
1067
|
|
|
// Is it a numeric, boolean or string value? |
1068
|
3 |
|
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) && ($arg != '')))) { |
1069
|
3 |
|
++$returnValue; |
1070
|
|
|
} |
1071
|
|
|
} |
1072
|
|
|
|
1073
|
3 |
|
return $returnValue; |
1074
|
|
|
} |
1075
|
|
|
|
1076
|
|
|
/** |
1077
|
|
|
* COUNTBLANK. |
1078
|
|
|
* |
1079
|
|
|
* Counts the number of empty cells within the list of arguments |
1080
|
|
|
* |
1081
|
|
|
* Excel Function: |
1082
|
|
|
* COUNTBLANK(value1[,value2[, ...]]) |
1083
|
|
|
* |
1084
|
|
|
* @category Statistical Functions |
1085
|
|
|
* |
1086
|
|
|
* @param mixed ...$args Data values |
1087
|
|
|
* |
1088
|
|
|
* @return int |
1089
|
|
|
*/ |
1090
|
|
|
public static function COUNTBLANK(...$args) |
1091
|
|
|
{ |
1092
|
|
|
$returnValue = 0; |
1093
|
|
|
|
1094
|
|
|
// Loop through arguments |
1095
|
|
|
$aArgs = Functions::flattenArray($args); |
1096
|
|
|
foreach ($aArgs as $arg) { |
1097
|
|
|
// Is it a blank cell? |
1098
|
|
|
if (($arg === null) || ((is_string($arg)) && ($arg == ''))) { |
1099
|
|
|
++$returnValue; |
1100
|
|
|
} |
1101
|
|
|
} |
1102
|
|
|
|
1103
|
|
|
return $returnValue; |
1104
|
|
|
} |
1105
|
|
|
|
1106
|
|
|
/** |
1107
|
|
|
* COUNTIF. |
1108
|
|
|
* |
1109
|
|
|
* Counts the number of cells that contain numbers within the list of arguments |
1110
|
|
|
* |
1111
|
|
|
* Excel Function: |
1112
|
|
|
* COUNTIF(value1[,value2[, ...]],condition) |
1113
|
|
|
* |
1114
|
|
|
* @category Statistical Functions |
1115
|
|
|
* |
1116
|
|
|
* @param mixed $aArgs Data values |
1117
|
|
|
* @param string $condition the criteria that defines which cells will be counted |
1118
|
|
|
* |
1119
|
|
|
* @return int |
1120
|
|
|
*/ |
1121
|
6 |
|
public static function COUNTIF($aArgs, $condition) |
1122
|
|
|
{ |
1123
|
6 |
|
$returnValue = 0; |
1124
|
|
|
|
1125
|
6 |
|
$aArgs = Functions::flattenArray($aArgs); |
1126
|
6 |
|
$condition = Functions::ifCondition($condition); |
1127
|
6 |
|
$conditionIsNumeric = strpos($condition, '"') === false; |
1128
|
|
|
// Loop through arguments |
1129
|
6 |
|
foreach ($aArgs as $arg) { |
1130
|
6 |
|
if (!is_numeric($arg)) { |
1131
|
4 |
|
if ($conditionIsNumeric) { |
1132
|
2 |
|
continue; |
1133
|
|
|
} |
1134
|
2 |
|
$arg = Calculation::wrapResult(strtoupper($arg)); |
1135
|
4 |
|
} elseif (!$conditionIsNumeric) { |
1136
|
|
|
continue; |
1137
|
|
|
} |
1138
|
6 |
|
$testCondition = '=' . $arg . $condition; |
1139
|
6 |
|
if (Calculation::getInstance()->_calculateFormulaValue($testCondition)) { |
1140
|
|
|
// Is it a value within our criteria |
1141
|
6 |
|
++$returnValue; |
1142
|
|
|
} |
1143
|
|
|
} |
1144
|
|
|
|
1145
|
6 |
|
return $returnValue; |
1146
|
|
|
} |
1147
|
|
|
|
1148
|
|
|
/** |
1149
|
|
|
* COUNTIFS. |
1150
|
|
|
* |
1151
|
|
|
* Counts the number of cells that contain numbers within the list of arguments |
1152
|
|
|
* |
1153
|
|
|
* Excel Function: |
1154
|
|
|
* COUNTIFS(criteria_range1, criteria1, [criteria_range2, criteria2]…) |
1155
|
|
|
* |
1156
|
|
|
* @category Statistical Functions |
1157
|
|
|
* |
1158
|
|
|
* @param mixed $args Criterias |
1159
|
|
|
* |
1160
|
|
|
* @return int |
1161
|
|
|
*/ |
1162
|
4 |
|
public static function COUNTIFS(...$args) |
1163
|
|
|
{ |
1164
|
4 |
|
$arrayList = $args; |
1165
|
|
|
|
1166
|
|
|
// Return value |
1167
|
4 |
|
$returnValue = 0; |
1168
|
|
|
|
1169
|
4 |
|
if (empty($arrayList)) { |
1170
|
|
|
return $returnValue; |
1171
|
|
|
} |
1172
|
|
|
|
1173
|
4 |
|
$aArgsArray = []; |
1174
|
4 |
|
$conditions = []; |
1175
|
|
|
|
1176
|
4 |
|
while (count($arrayList) > 0) { |
1177
|
4 |
|
$aArgsArray[] = Functions::flattenArray(array_shift($arrayList)); |
1178
|
4 |
|
$conditions[] = Functions::ifCondition(array_shift($arrayList)); |
1179
|
|
|
} |
1180
|
|
|
|
1181
|
|
|
// Loop through each arg and see if arguments and conditions are true |
1182
|
4 |
|
foreach (array_keys($aArgsArray[0]) as $index) { |
1183
|
4 |
|
$valid = true; |
1184
|
|
|
|
1185
|
4 |
|
foreach ($conditions as $cidx => $condition) { |
1186
|
4 |
|
$conditionIsNumeric = strpos($condition, '"') === false; |
1187
|
4 |
|
$arg = $aArgsArray[$cidx][$index]; |
1188
|
|
|
|
1189
|
|
|
// Loop through arguments |
1190
|
4 |
|
if (!is_numeric($arg)) { |
1191
|
4 |
|
if ($conditionIsNumeric) { |
1192
|
1 |
|
$valid = false; |
1193
|
|
|
|
1194
|
1 |
|
break; // if false found, don't need to check other conditions |
1195
|
|
|
} |
1196
|
3 |
|
$arg = Calculation::wrapResult(strtoupper($arg)); |
1197
|
1 |
|
} elseif (!$conditionIsNumeric) { |
1198
|
|
|
$valid = false; |
1199
|
|
|
|
1200
|
|
|
break; // if false found, don't need to check other conditions |
1201
|
|
|
} |
1202
|
4 |
|
$testCondition = '=' . $arg . $condition; |
1203
|
4 |
|
if (!Calculation::getInstance()->_calculateFormulaValue($testCondition)) { |
1204
|
|
|
// Is not a value within our criteria |
1205
|
4 |
|
$valid = false; |
1206
|
|
|
|
1207
|
4 |
|
break; // if false found, don't need to check other conditions |
1208
|
|
|
} |
1209
|
|
|
} |
1210
|
|
|
|
1211
|
4 |
|
if ($valid) { |
1212
|
4 |
|
++$returnValue; |
1213
|
|
|
} |
1214
|
|
|
} |
1215
|
|
|
|
1216
|
|
|
// Return |
1217
|
4 |
|
return $returnValue; |
1218
|
|
|
} |
1219
|
|
|
|
1220
|
|
|
/** |
1221
|
|
|
* COVAR. |
1222
|
|
|
* |
1223
|
|
|
* Returns covariance, the average of the products of deviations for each data point pair. |
1224
|
|
|
* |
1225
|
|
|
* @param mixed $yValues array of mixed Data Series Y |
1226
|
|
|
* @param mixed $xValues array of mixed Data Series X |
1227
|
|
|
* |
1228
|
|
|
* @return float |
1229
|
|
|
*/ |
1230
|
|
|
public static function COVAR($yValues, $xValues) |
1231
|
|
|
{ |
1232
|
|
|
if (!self::checkTrendArrays($yValues, $xValues)) { |
1233
|
|
|
return Functions::VALUE(); |
|
|
|
|
1234
|
|
|
} |
1235
|
|
|
$yValueCount = count($yValues); |
1236
|
|
|
$xValueCount = count($xValues); |
1237
|
|
|
|
1238
|
|
|
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) { |
1239
|
|
|
return Functions::NA(); |
|
|
|
|
1240
|
|
|
} elseif ($yValueCount == 1) { |
1241
|
|
|
return Functions::DIV0(); |
|
|
|
|
1242
|
|
|
} |
1243
|
|
|
|
1244
|
|
|
$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues); |
1245
|
|
|
|
1246
|
|
|
return $bestFitLinear->getCovariance(); |
1247
|
|
|
} |
1248
|
|
|
|
1249
|
|
|
/** |
1250
|
|
|
* CRITBINOM. |
1251
|
|
|
* |
1252
|
|
|
* Returns the smallest value for which the cumulative binomial distribution is greater |
1253
|
|
|
* than or equal to a criterion value |
1254
|
|
|
* |
1255
|
|
|
* See https://support.microsoft.com/en-us/help/828117/ for details of the algorithm used |
1256
|
|
|
* |
1257
|
|
|
* @param float $trials number of Bernoulli trials |
1258
|
|
|
* @param float $probability probability of a success on each trial |
1259
|
|
|
* @param float $alpha criterion value |
1260
|
|
|
* |
1261
|
|
|
* @return int |
1262
|
|
|
* |
1263
|
|
|
* @todo Warning. This implementation differs from the algorithm detailed on the MS |
1264
|
|
|
* web site in that $CumPGuessMinus1 = $CumPGuess - 1 rather than $CumPGuess - $PGuess |
1265
|
|
|
* This eliminates a potential endless loop error, but may have an adverse affect on the |
1266
|
|
|
* accuracy of the function (although all my tests have so far returned correct results). |
1267
|
|
|
*/ |
1268
|
|
|
public static function CRITBINOM($trials, $probability, $alpha) |
1269
|
|
|
{ |
1270
|
|
|
$trials = floor(Functions::flattenSingleValue($trials)); |
1271
|
|
|
$probability = Functions::flattenSingleValue($probability); |
1272
|
|
|
$alpha = Functions::flattenSingleValue($alpha); |
1273
|
|
|
|
1274
|
|
|
if ((is_numeric($trials)) && (is_numeric($probability)) && (is_numeric($alpha))) { |
1275
|
|
|
if ($trials < 0) { |
1276
|
|
|
return Functions::NAN(); |
|
|
|
|
1277
|
|
|
} elseif (($probability < 0) || ($probability > 1)) { |
1278
|
|
|
return Functions::NAN(); |
|
|
|
|
1279
|
|
|
} elseif (($alpha < 0) || ($alpha > 1)) { |
1280
|
|
|
return Functions::NAN(); |
|
|
|
|
1281
|
|
|
} elseif ($alpha <= 0.5) { |
1282
|
|
|
$t = sqrt(log(1 / ($alpha * $alpha))); |
1283
|
|
|
$trialsApprox = 0 - ($t + (2.515517 + 0.802853 * $t + 0.010328 * $t * $t) / (1 + 1.432788 * $t + 0.189269 * $t * $t + 0.001308 * $t * $t * $t)); |
1284
|
|
|
} else { |
1285
|
|
|
$t = sqrt(log(1 / pow(1 - $alpha, 2))); |
1286
|
|
|
$trialsApprox = $t - (2.515517 + 0.802853 * $t + 0.010328 * $t * $t) / (1 + 1.432788 * $t + 0.189269 * $t * $t + 0.001308 * $t * $t * $t); |
1287
|
|
|
} |
1288
|
|
|
$Guess = floor($trials * $probability + $trialsApprox * sqrt($trials * $probability * (1 - $probability))); |
1289
|
|
|
if ($Guess < 0) { |
1290
|
|
|
$Guess = 0; |
1291
|
|
|
} elseif ($Guess > $trials) { |
1292
|
|
|
$Guess = $trials; |
1293
|
|
|
} |
1294
|
|
|
|
1295
|
|
|
$TotalUnscaledProbability = $UnscaledPGuess = $UnscaledCumPGuess = 0.0; |
1296
|
|
|
$EssentiallyZero = 10e-12; |
1297
|
|
|
|
1298
|
|
|
$m = floor($trials * $probability); |
1299
|
|
|
++$TotalUnscaledProbability; |
1300
|
|
|
if ($m == $Guess) { |
1301
|
|
|
++$UnscaledPGuess; |
1302
|
|
|
} |
1303
|
|
|
if ($m <= $Guess) { |
1304
|
|
|
++$UnscaledCumPGuess; |
1305
|
|
|
} |
1306
|
|
|
|
1307
|
|
|
$PreviousValue = 1; |
1308
|
|
|
$Done = false; |
1309
|
|
|
$k = $m + 1; |
1310
|
|
|
while ((!$Done) && ($k <= $trials)) { |
1311
|
|
|
$CurrentValue = $PreviousValue * ($trials - $k + 1) * $probability / ($k * (1 - $probability)); |
1312
|
|
|
$TotalUnscaledProbability += $CurrentValue; |
1313
|
|
|
if ($k == $Guess) { |
1314
|
|
|
$UnscaledPGuess += $CurrentValue; |
1315
|
|
|
} |
1316
|
|
|
if ($k <= $Guess) { |
1317
|
|
|
$UnscaledCumPGuess += $CurrentValue; |
1318
|
|
|
} |
1319
|
|
|
if ($CurrentValue <= $EssentiallyZero) { |
1320
|
|
|
$Done = true; |
1321
|
|
|
} |
1322
|
|
|
$PreviousValue = $CurrentValue; |
1323
|
|
|
++$k; |
1324
|
|
|
} |
1325
|
|
|
|
1326
|
|
|
$PreviousValue = 1; |
1327
|
|
|
$Done = false; |
1328
|
|
|
$k = $m - 1; |
1329
|
|
|
while ((!$Done) && ($k >= 0)) { |
1330
|
|
|
$CurrentValue = $PreviousValue * $k + 1 * (1 - $probability) / (($trials - $k) * $probability); |
1331
|
|
|
$TotalUnscaledProbability += $CurrentValue; |
1332
|
|
|
if ($k == $Guess) { |
1333
|
|
|
$UnscaledPGuess += $CurrentValue; |
1334
|
|
|
} |
1335
|
|
|
if ($k <= $Guess) { |
1336
|
|
|
$UnscaledCumPGuess += $CurrentValue; |
1337
|
|
|
} |
1338
|
|
|
if ($CurrentValue <= $EssentiallyZero) { |
1339
|
|
|
$Done = true; |
1340
|
|
|
} |
1341
|
|
|
$PreviousValue = $CurrentValue; |
1342
|
|
|
--$k; |
1343
|
|
|
} |
1344
|
|
|
|
1345
|
|
|
$PGuess = $UnscaledPGuess / $TotalUnscaledProbability; |
1346
|
|
|
$CumPGuess = $UnscaledCumPGuess / $TotalUnscaledProbability; |
1347
|
|
|
|
1348
|
|
|
$CumPGuessMinus1 = $CumPGuess - 1; |
1349
|
|
|
|
1350
|
|
|
while (true) { |
1351
|
|
|
if (($CumPGuessMinus1 < $alpha) && ($CumPGuess >= $alpha)) { |
1352
|
|
|
return $Guess; |
1353
|
|
|
} elseif (($CumPGuessMinus1 < $alpha) && ($CumPGuess < $alpha)) { |
1354
|
|
|
$PGuessPlus1 = $PGuess * ($trials - $Guess) * $probability / $Guess / (1 - $probability); |
1355
|
|
|
$CumPGuessMinus1 = $CumPGuess; |
1356
|
|
|
$CumPGuess = $CumPGuess + $PGuessPlus1; |
1357
|
|
|
$PGuess = $PGuessPlus1; |
1358
|
|
|
++$Guess; |
1359
|
|
|
} elseif (($CumPGuessMinus1 >= $alpha) && ($CumPGuess >= $alpha)) { |
1360
|
|
|
$PGuessMinus1 = $PGuess * $Guess * (1 - $probability) / ($trials - $Guess + 1) / $probability; |
1361
|
|
|
$CumPGuess = $CumPGuessMinus1; |
1362
|
|
|
$CumPGuessMinus1 = $CumPGuessMinus1 - $PGuess; |
1363
|
|
|
$PGuess = $PGuessMinus1; |
1364
|
|
|
--$Guess; |
1365
|
|
|
} |
1366
|
|
|
} |
1367
|
|
|
} |
1368
|
|
|
|
1369
|
|
|
return Functions::VALUE(); |
|
|
|
|
1370
|
|
|
} |
1371
|
|
|
|
1372
|
|
|
/** |
1373
|
|
|
* DEVSQ. |
1374
|
|
|
* |
1375
|
|
|
* Returns the sum of squares of deviations of data points from their sample mean. |
1376
|
|
|
* |
1377
|
|
|
* Excel Function: |
1378
|
|
|
* DEVSQ(value1[,value2[, ...]]) |
1379
|
|
|
* |
1380
|
|
|
* @category Statistical Functions |
1381
|
|
|
* |
1382
|
|
|
* @param mixed ...$args Data values |
1383
|
|
|
* |
1384
|
|
|
* @return float|string |
1385
|
|
|
*/ |
1386
|
1 |
|
public static function DEVSQ(...$args) |
1387
|
|
|
{ |
1388
|
1 |
|
$aArgs = Functions::flattenArrayIndexed($args); |
1389
|
|
|
|
1390
|
|
|
// Return value |
1391
|
1 |
|
$returnValue = null; |
1392
|
|
|
|
1393
|
1 |
|
$aMean = self::AVERAGE($aArgs); |
1394
|
1 |
|
if ($aMean != Functions::DIV0()) { |
1395
|
1 |
|
$aCount = -1; |
1396
|
1 |
|
foreach ($aArgs as $k => $arg) { |
1397
|
|
|
// Is it a numeric value? |
1398
|
1 |
|
if ((is_bool($arg)) && |
1399
|
1 |
|
((!Functions::isCellValue($k)) || |
1400
|
1 |
|
(Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE))) { |
1401
|
|
|
$arg = (int) $arg; |
1402
|
|
|
} |
1403
|
1 |
|
if ((is_numeric($arg)) && (!is_string($arg))) { |
1404
|
1 |
|
if ($returnValue === null) { |
1405
|
1 |
|
$returnValue = pow(($arg - $aMean), 2); |
1406
|
|
|
} else { |
1407
|
1 |
|
$returnValue += pow(($arg - $aMean), 2); |
1408
|
|
|
} |
1409
|
1 |
|
++$aCount; |
1410
|
|
|
} |
1411
|
|
|
} |
1412
|
|
|
|
1413
|
|
|
// Return |
1414
|
1 |
|
if ($returnValue === null) { |
1415
|
|
|
return Functions::NAN(); |
1416
|
|
|
} |
1417
|
|
|
|
1418
|
1 |
|
return $returnValue; |
1419
|
|
|
} |
1420
|
|
|
|
1421
|
|
|
return self::NA(); |
|
|
|
|
1422
|
|
|
} |
1423
|
|
|
|
1424
|
|
|
/** |
1425
|
|
|
* EXPONDIST. |
1426
|
|
|
* |
1427
|
|
|
* Returns the exponential distribution. Use EXPONDIST to model the time between events, |
1428
|
|
|
* such as how long an automated bank teller takes to deliver cash. For example, you can |
1429
|
|
|
* use EXPONDIST to determine the probability that the process takes at most 1 minute. |
1430
|
|
|
* |
1431
|
|
|
* @param float $value Value of the function |
1432
|
|
|
* @param float $lambda The parameter value |
1433
|
|
|
* @param bool $cumulative |
1434
|
|
|
* |
1435
|
|
|
* @return float |
1436
|
|
|
*/ |
1437
|
|
|
public static function EXPONDIST($value, $lambda, $cumulative) |
1438
|
|
|
{ |
1439
|
|
|
$value = Functions::flattenSingleValue($value); |
1440
|
|
|
$lambda = Functions::flattenSingleValue($lambda); |
1441
|
|
|
$cumulative = Functions::flattenSingleValue($cumulative); |
1442
|
|
|
|
1443
|
|
|
if ((is_numeric($value)) && (is_numeric($lambda))) { |
1444
|
|
|
if (($value < 0) || ($lambda < 0)) { |
1445
|
|
|
return Functions::NAN(); |
|
|
|
|
1446
|
|
|
} |
1447
|
|
|
if ((is_numeric($cumulative)) || (is_bool($cumulative))) { |
1448
|
|
|
if ($cumulative) { |
1449
|
|
|
return 1 - exp(0 - $value * $lambda); |
1450
|
|
|
} |
1451
|
|
|
|
1452
|
|
|
return $lambda * exp(0 - $value * $lambda); |
1453
|
|
|
} |
1454
|
|
|
} |
1455
|
|
|
|
1456
|
|
|
return Functions::VALUE(); |
|
|
|
|
1457
|
|
|
} |
1458
|
|
|
|
1459
|
|
|
/** |
1460
|
|
|
* FISHER. |
1461
|
|
|
* |
1462
|
|
|
* Returns the Fisher transformation at x. This transformation produces a function that |
1463
|
|
|
* is normally distributed rather than skewed. Use this function to perform hypothesis |
1464
|
|
|
* testing on the correlation coefficient. |
1465
|
|
|
* |
1466
|
|
|
* @param float $value |
1467
|
|
|
* |
1468
|
|
|
* @return float |
1469
|
|
|
*/ |
1470
|
|
|
public static function FISHER($value) |
1471
|
|
|
{ |
1472
|
|
|
$value = Functions::flattenSingleValue($value); |
1473
|
|
|
|
1474
|
|
|
if (is_numeric($value)) { |
1475
|
|
|
if (($value <= -1) || ($value >= 1)) { |
1476
|
|
|
return Functions::NAN(); |
|
|
|
|
1477
|
|
|
} |
1478
|
|
|
|
1479
|
|
|
return 0.5 * log((1 + $value) / (1 - $value)); |
1480
|
|
|
} |
1481
|
|
|
|
1482
|
|
|
return Functions::VALUE(); |
|
|
|
|
1483
|
|
|
} |
1484
|
|
|
|
1485
|
|
|
/** |
1486
|
|
|
* FISHERINV. |
1487
|
|
|
* |
1488
|
|
|
* Returns the inverse of the Fisher transformation. Use this transformation when |
1489
|
|
|
* analyzing correlations between ranges or arrays of data. If y = FISHER(x), then |
1490
|
|
|
* FISHERINV(y) = x. |
1491
|
|
|
* |
1492
|
|
|
* @param float $value |
1493
|
|
|
* |
1494
|
|
|
* @return float |
1495
|
|
|
*/ |
1496
|
|
|
public static function FISHERINV($value) |
1497
|
|
|
{ |
1498
|
|
|
$value = Functions::flattenSingleValue($value); |
1499
|
|
|
|
1500
|
|
|
if (is_numeric($value)) { |
1501
|
|
|
return (exp(2 * $value) - 1) / (exp(2 * $value) + 1); |
1502
|
|
|
} |
1503
|
|
|
|
1504
|
|
|
return Functions::VALUE(); |
|
|
|
|
1505
|
|
|
} |
1506
|
|
|
|
1507
|
|
|
/** |
1508
|
|
|
* FORECAST. |
1509
|
|
|
* |
1510
|
|
|
* Calculates, or predicts, a future value by using existing values. The predicted value is a y-value for a given x-value. |
1511
|
|
|
* |
1512
|
|
|
* @param float $xValue Value of X for which we want to find Y |
1513
|
|
|
* @param mixed $yValues array of mixed Data Series Y |
1514
|
|
|
* @param mixed $xValues of mixed Data Series X |
1515
|
|
|
* |
1516
|
|
|
* @return float |
1517
|
|
|
*/ |
1518
|
|
|
public static function FORECAST($xValue, $yValues, $xValues) |
1519
|
|
|
{ |
1520
|
|
|
$xValue = Functions::flattenSingleValue($xValue); |
1521
|
|
|
if (!is_numeric($xValue)) { |
1522
|
|
|
return Functions::VALUE(); |
|
|
|
|
1523
|
|
|
} elseif (!self::checkTrendArrays($yValues, $xValues)) { |
1524
|
|
|
return Functions::VALUE(); |
|
|
|
|
1525
|
|
|
} |
1526
|
|
|
$yValueCount = count($yValues); |
1527
|
|
|
$xValueCount = count($xValues); |
1528
|
|
|
|
1529
|
|
|
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) { |
1530
|
|
|
return Functions::NA(); |
|
|
|
|
1531
|
|
|
} elseif ($yValueCount == 1) { |
1532
|
|
|
return Functions::DIV0(); |
|
|
|
|
1533
|
|
|
} |
1534
|
|
|
|
1535
|
|
|
$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues); |
1536
|
|
|
|
1537
|
|
|
return $bestFitLinear->getValueOfYForX($xValue); |
|
|
|
|
1538
|
|
|
} |
1539
|
|
|
|
1540
|
|
|
/** |
1541
|
|
|
* GAMMADIST. |
1542
|
|
|
* |
1543
|
|
|
* Returns the gamma distribution. |
1544
|
|
|
* |
1545
|
|
|
* @param float $value Value at which you want to evaluate the distribution |
1546
|
|
|
* @param float $a Parameter to the distribution |
1547
|
|
|
* @param float $b Parameter to the distribution |
1548
|
|
|
* @param bool $cumulative |
1549
|
|
|
* |
1550
|
|
|
* @return float |
1551
|
|
|
*/ |
1552
|
|
|
public static function GAMMADIST($value, $a, $b, $cumulative) |
1553
|
|
|
{ |
1554
|
|
|
$value = Functions::flattenSingleValue($value); |
1555
|
|
|
$a = Functions::flattenSingleValue($a); |
1556
|
|
|
$b = Functions::flattenSingleValue($b); |
1557
|
|
|
|
1558
|
|
|
if ((is_numeric($value)) && (is_numeric($a)) && (is_numeric($b))) { |
1559
|
|
|
if (($value < 0) || ($a <= 0) || ($b <= 0)) { |
1560
|
|
|
return Functions::NAN(); |
|
|
|
|
1561
|
|
|
} |
1562
|
|
|
if ((is_numeric($cumulative)) || (is_bool($cumulative))) { |
|
|
|
|
1563
|
|
|
if ($cumulative) { |
1564
|
|
|
return self::incompleteGamma($a, $value / $b) / self::gamma($a); |
1565
|
|
|
} |
1566
|
|
|
|
1567
|
|
|
return (1 / (pow($b, $a) * self::gamma($a))) * pow($value, $a - 1) * exp(0 - ($value / $b)); |
1568
|
|
|
} |
1569
|
|
|
} |
1570
|
|
|
|
1571
|
|
|
return Functions::VALUE(); |
|
|
|
|
1572
|
|
|
} |
1573
|
|
|
|
1574
|
|
|
/** |
1575
|
|
|
* GAMMAINV. |
1576
|
|
|
* |
1577
|
|
|
* Returns the inverse of the beta distribution. |
1578
|
|
|
* |
1579
|
|
|
* @param float $probability Probability at which you want to evaluate the distribution |
1580
|
|
|
* @param float $alpha Parameter to the distribution |
1581
|
|
|
* @param float $beta Parameter to the distribution |
1582
|
|
|
* |
1583
|
|
|
* @return float |
1584
|
|
|
*/ |
1585
|
|
|
public static function GAMMAINV($probability, $alpha, $beta) |
1586
|
|
|
{ |
1587
|
|
|
$probability = Functions::flattenSingleValue($probability); |
1588
|
|
|
$alpha = Functions::flattenSingleValue($alpha); |
1589
|
|
|
$beta = Functions::flattenSingleValue($beta); |
1590
|
|
|
|
1591
|
|
|
if ((is_numeric($probability)) && (is_numeric($alpha)) && (is_numeric($beta))) { |
1592
|
|
|
if (($alpha <= 0) || ($beta <= 0) || ($probability < 0) || ($probability > 1)) { |
1593
|
|
|
return Functions::NAN(); |
|
|
|
|
1594
|
|
|
} |
1595
|
|
|
|
1596
|
|
|
$xLo = 0; |
1597
|
|
|
$xHi = $alpha * $beta * 5; |
1598
|
|
|
|
1599
|
|
|
$x = $xNew = 1; |
1600
|
|
|
$error = $pdf = 0; |
|
|
|
|
1601
|
|
|
$dx = 1024; |
1602
|
|
|
$i = 0; |
1603
|
|
|
|
1604
|
|
|
while ((abs($dx) > Functions::PRECISION) && ($i++ < self::MAX_ITERATIONS)) { |
1605
|
|
|
// Apply Newton-Raphson step |
1606
|
|
|
$error = self::GAMMADIST($x, $alpha, $beta, true) - $probability; |
1607
|
|
|
if ($error < 0.0) { |
1608
|
|
|
$xLo = $x; |
1609
|
|
|
} else { |
1610
|
|
|
$xHi = $x; |
1611
|
|
|
} |
1612
|
|
|
$pdf = self::GAMMADIST($x, $alpha, $beta, false); |
1613
|
|
|
// Avoid division by zero |
1614
|
|
|
if ($pdf != 0.0) { |
1615
|
|
|
$dx = $error / $pdf; |
1616
|
|
|
$xNew = $x - $dx; |
1617
|
|
|
} |
1618
|
|
|
// If the NR fails to converge (which for example may be the |
1619
|
|
|
// case if the initial guess is too rough) we apply a bisection |
1620
|
|
|
// step to determine a more narrow interval around the root. |
1621
|
|
|
if (($xNew < $xLo) || ($xNew > $xHi) || ($pdf == 0.0)) { |
1622
|
|
|
$xNew = ($xLo + $xHi) / 2; |
1623
|
|
|
$dx = $xNew - $x; |
1624
|
|
|
} |
1625
|
|
|
$x = $xNew; |
1626
|
|
|
} |
1627
|
|
|
if ($i == self::MAX_ITERATIONS) { |
1628
|
|
|
return Functions::NA(); |
|
|
|
|
1629
|
|
|
} |
1630
|
|
|
|
1631
|
|
|
return $x; |
1632
|
|
|
} |
1633
|
|
|
|
1634
|
|
|
return Functions::VALUE(); |
|
|
|
|
1635
|
|
|
} |
1636
|
|
|
|
1637
|
|
|
/** |
1638
|
|
|
* GAMMALN. |
1639
|
|
|
* |
1640
|
|
|
* Returns the natural logarithm of the gamma function. |
1641
|
|
|
* |
1642
|
|
|
* @param float $value |
1643
|
|
|
* |
1644
|
|
|
* @return float |
1645
|
|
|
*/ |
1646
|
|
|
public static function GAMMALN($value) |
1647
|
|
|
{ |
1648
|
|
|
$value = Functions::flattenSingleValue($value); |
1649
|
|
|
|
1650
|
|
|
if (is_numeric($value)) { |
1651
|
|
|
if ($value <= 0) { |
1652
|
|
|
return Functions::NAN(); |
|
|
|
|
1653
|
|
|
} |
1654
|
|
|
|
1655
|
|
|
return log(self::gamma($value)); |
1656
|
|
|
} |
1657
|
|
|
|
1658
|
|
|
return Functions::VALUE(); |
|
|
|
|
1659
|
|
|
} |
1660
|
|
|
|
1661
|
|
|
/** |
1662
|
|
|
* GEOMEAN. |
1663
|
|
|
* |
1664
|
|
|
* Returns the geometric mean of an array or range of positive data. For example, you |
1665
|
|
|
* can use GEOMEAN to calculate average growth rate given compound interest with |
1666
|
|
|
* variable rates. |
1667
|
|
|
* |
1668
|
|
|
* Excel Function: |
1669
|
|
|
* GEOMEAN(value1[,value2[, ...]]) |
1670
|
|
|
* |
1671
|
|
|
* @category Statistical Functions |
1672
|
|
|
* |
1673
|
|
|
* @param mixed ...$args Data values |
1674
|
|
|
* |
1675
|
|
|
* @return float |
1676
|
|
|
*/ |
1677
|
|
|
public static function GEOMEAN(...$args) |
1678
|
|
|
{ |
1679
|
|
|
$aArgs = Functions::flattenArray($args); |
1680
|
|
|
|
1681
|
|
|
$aMean = MathTrig::PRODUCT($aArgs); |
1682
|
|
|
if (is_numeric($aMean) && ($aMean > 0)) { |
1683
|
|
|
$aCount = self::COUNT($aArgs); |
1684
|
|
|
if (self::MIN($aArgs) > 0) { |
1685
|
|
|
return pow($aMean, (1 / $aCount)); |
1686
|
|
|
} |
1687
|
|
|
} |
1688
|
|
|
|
1689
|
|
|
return Functions::NAN(); |
|
|
|
|
1690
|
|
|
} |
1691
|
|
|
|
1692
|
|
|
/** |
1693
|
|
|
* GROWTH. |
1694
|
|
|
* |
1695
|
|
|
* Returns values along a predicted emponential Trend |
1696
|
|
|
* |
1697
|
|
|
* @param mixed[] $yValues Data Series Y |
1698
|
|
|
* @param mixed[] $xValues Data Series X |
1699
|
|
|
* @param mixed[] $newValues Values of X for which we want to find Y |
1700
|
|
|
* @param bool $const a logical value specifying whether to force the intersect to equal 0 |
1701
|
|
|
* |
1702
|
|
|
* @return array of float |
1703
|
|
|
*/ |
1704
|
|
|
public static function GROWTH($yValues, $xValues = [], $newValues = [], $const = true) |
1705
|
|
|
{ |
1706
|
|
|
$yValues = Functions::flattenArray($yValues); |
1707
|
|
|
$xValues = Functions::flattenArray($xValues); |
1708
|
|
|
$newValues = Functions::flattenArray($newValues); |
1709
|
|
|
$const = ($const === null) ? true : (bool) Functions::flattenSingleValue($const); |
|
|
|
|
1710
|
|
|
|
1711
|
|
|
$bestFitExponential = Trend::calculate(Trend::TREND_EXPONENTIAL, $yValues, $xValues, $const); |
1712
|
|
|
if (empty($newValues)) { |
1713
|
|
|
$newValues = $bestFitExponential->getXValues(); |
1714
|
|
|
} |
1715
|
|
|
|
1716
|
|
|
$returnArray = []; |
1717
|
|
|
foreach ($newValues as $xValue) { |
1718
|
|
|
$returnArray[0][] = $bestFitExponential->getValueOfYForX($xValue); |
1719
|
|
|
} |
1720
|
|
|
|
1721
|
|
|
return $returnArray; |
1722
|
|
|
} |
1723
|
|
|
|
1724
|
|
|
/** |
1725
|
|
|
* HARMEAN. |
1726
|
|
|
* |
1727
|
|
|
* Returns the harmonic mean of a data set. The harmonic mean is the reciprocal of the |
1728
|
|
|
* arithmetic mean of reciprocals. |
1729
|
|
|
* |
1730
|
|
|
* Excel Function: |
1731
|
|
|
* HARMEAN(value1[,value2[, ...]]) |
1732
|
|
|
* |
1733
|
|
|
* @category Statistical Functions |
1734
|
|
|
* |
1735
|
|
|
* @param mixed ...$args Data values |
1736
|
|
|
* |
1737
|
|
|
* @return float |
1738
|
|
|
*/ |
1739
|
|
|
public static function HARMEAN(...$args) |
1740
|
|
|
{ |
1741
|
|
|
// Return value |
1742
|
|
|
$returnValue = Functions::NA(); |
1743
|
|
|
|
1744
|
|
|
// Loop through arguments |
1745
|
|
|
$aArgs = Functions::flattenArray($args); |
1746
|
|
|
if (self::MIN($aArgs) < 0) { |
1747
|
|
|
return Functions::NAN(); |
|
|
|
|
1748
|
|
|
} |
1749
|
|
|
$aCount = 0; |
1750
|
|
|
foreach ($aArgs as $arg) { |
1751
|
|
|
// Is it a numeric value? |
1752
|
|
|
if ((is_numeric($arg)) && (!is_string($arg))) { |
1753
|
|
|
if ($arg <= 0) { |
1754
|
|
|
return Functions::NAN(); |
|
|
|
|
1755
|
|
|
} |
1756
|
|
|
if ($returnValue === null) { |
1757
|
|
|
$returnValue = (1 / $arg); |
1758
|
|
|
} else { |
1759
|
|
|
$returnValue += (1 / $arg); |
1760
|
|
|
} |
1761
|
|
|
++$aCount; |
1762
|
|
|
} |
1763
|
|
|
} |
1764
|
|
|
|
1765
|
|
|
// Return |
1766
|
|
|
if ($aCount > 0) { |
1767
|
|
|
return 1 / ($returnValue / $aCount); |
1768
|
|
|
} |
1769
|
|
|
|
1770
|
|
|
return $returnValue; |
|
|
|
|
1771
|
|
|
} |
1772
|
|
|
|
1773
|
|
|
/** |
1774
|
|
|
* HYPGEOMDIST. |
1775
|
|
|
* |
1776
|
|
|
* Returns the hypergeometric distribution. HYPGEOMDIST returns the probability of a given number of |
1777
|
|
|
* sample successes, given the sample size, population successes, and population size. |
1778
|
|
|
* |
1779
|
|
|
* @param float $sampleSuccesses Number of successes in the sample |
1780
|
|
|
* @param float $sampleNumber Size of the sample |
1781
|
|
|
* @param float $populationSuccesses Number of successes in the population |
1782
|
|
|
* @param float $populationNumber Population size |
1783
|
|
|
* |
1784
|
|
|
* @return float |
1785
|
|
|
*/ |
1786
|
|
|
public static function HYPGEOMDIST($sampleSuccesses, $sampleNumber, $populationSuccesses, $populationNumber) |
1787
|
|
|
{ |
1788
|
|
|
$sampleSuccesses = floor(Functions::flattenSingleValue($sampleSuccesses)); |
1789
|
|
|
$sampleNumber = floor(Functions::flattenSingleValue($sampleNumber)); |
1790
|
|
|
$populationSuccesses = floor(Functions::flattenSingleValue($populationSuccesses)); |
1791
|
|
|
$populationNumber = floor(Functions::flattenSingleValue($populationNumber)); |
1792
|
|
|
|
1793
|
|
|
if ((is_numeric($sampleSuccesses)) && (is_numeric($sampleNumber)) && (is_numeric($populationSuccesses)) && (is_numeric($populationNumber))) { |
|
|
|
|
1794
|
|
|
if (($sampleSuccesses < 0) || ($sampleSuccesses > $sampleNumber) || ($sampleSuccesses > $populationSuccesses)) { |
1795
|
|
|
return Functions::NAN(); |
|
|
|
|
1796
|
|
|
} |
1797
|
|
|
if (($sampleNumber <= 0) || ($sampleNumber > $populationNumber)) { |
1798
|
|
|
return Functions::NAN(); |
|
|
|
|
1799
|
|
|
} |
1800
|
|
|
if (($populationSuccesses <= 0) || ($populationSuccesses > $populationNumber)) { |
1801
|
|
|
return Functions::NAN(); |
|
|
|
|
1802
|
|
|
} |
1803
|
|
|
|
1804
|
|
|
return MathTrig::COMBIN($populationSuccesses, $sampleSuccesses) * |
|
|
|
|
1805
|
|
|
MathTrig::COMBIN($populationNumber - $populationSuccesses, $sampleNumber - $sampleSuccesses) / |
1806
|
|
|
MathTrig::COMBIN($populationNumber, $sampleNumber); |
1807
|
|
|
} |
1808
|
|
|
|
1809
|
|
|
return Functions::VALUE(); |
1810
|
|
|
} |
1811
|
|
|
|
1812
|
|
|
/** |
1813
|
|
|
* INTERCEPT. |
1814
|
|
|
* |
1815
|
|
|
* Calculates the point at which a line will intersect the y-axis by using existing x-values and y-values. |
1816
|
|
|
* |
1817
|
|
|
* @param mixed[] $yValues Data Series Y |
1818
|
|
|
* @param mixed[] $xValues Data Series X |
1819
|
|
|
* |
1820
|
|
|
* @return float |
1821
|
|
|
*/ |
1822
|
|
|
public static function INTERCEPT($yValues, $xValues) |
1823
|
|
|
{ |
1824
|
|
|
if (!self::checkTrendArrays($yValues, $xValues)) { |
1825
|
|
|
return Functions::VALUE(); |
|
|
|
|
1826
|
|
|
} |
1827
|
|
|
$yValueCount = count($yValues); |
1828
|
|
|
$xValueCount = count($xValues); |
1829
|
|
|
|
1830
|
|
|
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) { |
1831
|
|
|
return Functions::NA(); |
|
|
|
|
1832
|
|
|
} elseif ($yValueCount == 1) { |
1833
|
|
|
return Functions::DIV0(); |
|
|
|
|
1834
|
|
|
} |
1835
|
|
|
|
1836
|
|
|
$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues); |
1837
|
|
|
|
1838
|
|
|
return $bestFitLinear->getIntersect(); |
1839
|
|
|
} |
1840
|
|
|
|
1841
|
|
|
/** |
1842
|
|
|
* KURT. |
1843
|
|
|
* |
1844
|
|
|
* Returns the kurtosis of a data set. Kurtosis characterizes the relative peakedness |
1845
|
|
|
* or flatness of a distribution compared with the normal distribution. Positive |
1846
|
|
|
* kurtosis indicates a relatively peaked distribution. Negative kurtosis indicates a |
1847
|
|
|
* relatively flat distribution. |
1848
|
|
|
* |
1849
|
|
|
* @param array ...$args Data Series |
1850
|
|
|
* |
1851
|
|
|
* @return float|string |
1852
|
|
|
*/ |
1853
|
|
|
public static function KURT(...$args) |
1854
|
|
|
{ |
1855
|
|
|
$aArgs = Functions::flattenArrayIndexed($args); |
1856
|
|
|
$mean = self::AVERAGE($aArgs); |
1857
|
|
|
$stdDev = self::STDEV($aArgs); |
1858
|
|
|
|
1859
|
|
|
if ($stdDev > 0) { |
1860
|
|
|
$count = $summer = 0; |
1861
|
|
|
// Loop through arguments |
1862
|
|
|
foreach ($aArgs as $k => $arg) { |
1863
|
|
|
if ((is_bool($arg)) && |
1864
|
|
|
(!Functions::isMatrixValue($k))) { |
1865
|
|
|
} else { |
1866
|
|
|
// Is it a numeric value? |
1867
|
|
|
if ((is_numeric($arg)) && (!is_string($arg))) { |
1868
|
|
|
$summer += pow((($arg - $mean) / $stdDev), 4); |
1869
|
|
|
++$count; |
1870
|
|
|
} |
1871
|
|
|
} |
1872
|
|
|
} |
1873
|
|
|
|
1874
|
|
|
// Return |
1875
|
|
|
if ($count > 3) { |
1876
|
|
|
return $summer * ($count * ($count + 1) / (($count - 1) * ($count - 2) * ($count - 3))) - (3 * pow($count - 1, 2) / (($count - 2) * ($count - 3))); |
1877
|
|
|
} |
1878
|
|
|
} |
1879
|
|
|
|
1880
|
|
|
return Functions::DIV0(); |
1881
|
|
|
} |
1882
|
|
|
|
1883
|
|
|
/** |
1884
|
|
|
* LARGE. |
1885
|
|
|
* |
1886
|
|
|
* Returns the nth largest value in a data set. You can use this function to |
1887
|
|
|
* select a value based on its relative standing. |
1888
|
|
|
* |
1889
|
|
|
* Excel Function: |
1890
|
|
|
* LARGE(value1[,value2[, ...]],entry) |
1891
|
|
|
* |
1892
|
|
|
* @category Statistical Functions |
1893
|
|
|
* |
1894
|
|
|
* @param mixed $args Data values |
1895
|
|
|
* @param int $entry Position (ordered from the largest) in the array or range of data to return |
1896
|
|
|
* |
1897
|
|
|
* @return float |
1898
|
|
|
*/ |
1899
|
|
|
public static function LARGE(...$args) |
1900
|
|
|
{ |
1901
|
|
|
$aArgs = Functions::flattenArray($args); |
1902
|
|
|
|
1903
|
|
|
// Calculate |
1904
|
|
|
$entry = floor(array_pop($aArgs)); |
1905
|
|
|
|
1906
|
|
|
if ((is_numeric($entry)) && (!is_string($entry))) { |
|
|
|
|
1907
|
|
|
$mArgs = []; |
1908
|
|
|
foreach ($aArgs as $arg) { |
1909
|
|
|
// Is it a numeric value? |
1910
|
|
|
if ((is_numeric($arg)) && (!is_string($arg))) { |
1911
|
|
|
$mArgs[] = $arg; |
1912
|
|
|
} |
1913
|
|
|
} |
1914
|
|
|
$count = self::COUNT($mArgs); |
1915
|
|
|
$entry = floor(--$entry); |
1916
|
|
|
if (($entry < 0) || ($entry >= $count) || ($count == 0)) { |
1917
|
|
|
return Functions::NAN(); |
|
|
|
|
1918
|
|
|
} |
1919
|
|
|
rsort($mArgs); |
1920
|
|
|
|
1921
|
|
|
return $mArgs[$entry]; |
1922
|
|
|
} |
1923
|
|
|
|
1924
|
|
|
return Functions::VALUE(); |
1925
|
|
|
} |
1926
|
|
|
|
1927
|
|
|
/** |
1928
|
|
|
* LINEST. |
1929
|
|
|
* |
1930
|
|
|
* Calculates the statistics for a line by using the "least squares" method to calculate a straight line that best fits your data, |
1931
|
|
|
* and then returns an array that describes the line. |
1932
|
|
|
* |
1933
|
|
|
* @param mixed[] $yValues Data Series Y |
1934
|
|
|
* @param null|mixed[] $xValues Data Series X |
1935
|
|
|
* @param bool $const a logical value specifying whether to force the intersect to equal 0 |
1936
|
|
|
* @param bool $stats a logical value specifying whether to return additional regression statistics |
1937
|
|
|
* |
1938
|
|
|
* @return array |
1939
|
|
|
*/ |
1940
|
|
|
public static function LINEST($yValues, $xValues = null, $const = true, $stats = false) |
1941
|
|
|
{ |
1942
|
|
|
$const = ($const === null) ? true : (bool) Functions::flattenSingleValue($const); |
|
|
|
|
1943
|
|
|
$stats = ($stats === null) ? false : (bool) Functions::flattenSingleValue($stats); |
|
|
|
|
1944
|
|
|
if ($xValues === null) { |
1945
|
|
|
$xValues = range(1, count(Functions::flattenArray($yValues))); |
1946
|
|
|
} |
1947
|
|
|
|
1948
|
|
|
if (!self::checkTrendArrays($yValues, $xValues)) { |
1949
|
|
|
return Functions::VALUE(); |
|
|
|
|
1950
|
|
|
} |
1951
|
|
|
$yValueCount = count($yValues); |
1952
|
|
|
$xValueCount = count($xValues); |
1953
|
|
|
|
1954
|
|
|
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) { |
1955
|
|
|
return Functions::NA(); |
|
|
|
|
1956
|
|
|
} elseif ($yValueCount == 1) { |
1957
|
|
|
return 0; |
|
|
|
|
1958
|
|
|
} |
1959
|
|
|
|
1960
|
|
|
$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues, $const); |
1961
|
|
|
if ($stats) { |
1962
|
|
|
return [ |
1963
|
|
|
[ |
1964
|
|
|
$bestFitLinear->getSlope(), |
1965
|
|
|
$bestFitLinear->getSlopeSE(), |
1966
|
|
|
$bestFitLinear->getGoodnessOfFit(), |
1967
|
|
|
$bestFitLinear->getF(), |
1968
|
|
|
$bestFitLinear->getSSRegression(), |
1969
|
|
|
], |
1970
|
|
|
[ |
1971
|
|
|
$bestFitLinear->getIntersect(), |
1972
|
|
|
$bestFitLinear->getIntersectSE(), |
1973
|
|
|
$bestFitLinear->getStdevOfResiduals(), |
1974
|
|
|
$bestFitLinear->getDFResiduals(), |
1975
|
|
|
$bestFitLinear->getSSResiduals(), |
1976
|
|
|
], |
1977
|
|
|
]; |
1978
|
|
|
} |
1979
|
|
|
|
1980
|
|
|
return [ |
1981
|
|
|
$bestFitLinear->getSlope(), |
1982
|
|
|
$bestFitLinear->getIntersect(), |
1983
|
|
|
]; |
1984
|
|
|
} |
1985
|
|
|
|
1986
|
|
|
/** |
1987
|
|
|
* LOGEST. |
1988
|
|
|
* |
1989
|
|
|
* Calculates an exponential curve that best fits the X and Y data series, |
1990
|
|
|
* and then returns an array that describes the line. |
1991
|
|
|
* |
1992
|
|
|
* @param mixed[] $yValues Data Series Y |
1993
|
|
|
* @param null|mixed[] $xValues Data Series X |
1994
|
|
|
* @param bool $const a logical value specifying whether to force the intersect to equal 0 |
1995
|
|
|
* @param bool $stats a logical value specifying whether to return additional regression statistics |
1996
|
|
|
* |
1997
|
|
|
* @return array |
1998
|
|
|
*/ |
1999
|
|
|
public static function LOGEST($yValues, $xValues = null, $const = true, $stats = false) |
2000
|
|
|
{ |
2001
|
|
|
$const = ($const === null) ? true : (bool) Functions::flattenSingleValue($const); |
|
|
|
|
2002
|
|
|
$stats = ($stats === null) ? false : (bool) Functions::flattenSingleValue($stats); |
|
|
|
|
2003
|
|
|
if ($xValues === null) { |
2004
|
|
|
$xValues = range(1, count(Functions::flattenArray($yValues))); |
2005
|
|
|
} |
2006
|
|
|
|
2007
|
|
|
if (!self::checkTrendArrays($yValues, $xValues)) { |
2008
|
|
|
return Functions::VALUE(); |
|
|
|
|
2009
|
|
|
} |
2010
|
|
|
$yValueCount = count($yValues); |
2011
|
|
|
$xValueCount = count($xValues); |
2012
|
|
|
|
2013
|
|
|
foreach ($yValues as $value) { |
2014
|
|
|
if ($value <= 0.0) { |
2015
|
|
|
return Functions::NAN(); |
|
|
|
|
2016
|
|
|
} |
2017
|
|
|
} |
2018
|
|
|
|
2019
|
|
|
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) { |
2020
|
|
|
return Functions::NA(); |
|
|
|
|
2021
|
|
|
} elseif ($yValueCount == 1) { |
2022
|
|
|
return 1; |
|
|
|
|
2023
|
|
|
} |
2024
|
|
|
|
2025
|
|
|
$bestFitExponential = Trend::calculate(Trend::TREND_EXPONENTIAL, $yValues, $xValues, $const); |
2026
|
|
|
if ($stats) { |
2027
|
|
|
return [ |
2028
|
|
|
[ |
2029
|
|
|
$bestFitExponential->getSlope(), |
2030
|
|
|
$bestFitExponential->getSlopeSE(), |
2031
|
|
|
$bestFitExponential->getGoodnessOfFit(), |
2032
|
|
|
$bestFitExponential->getF(), |
2033
|
|
|
$bestFitExponential->getSSRegression(), |
2034
|
|
|
], |
2035
|
|
|
[ |
2036
|
|
|
$bestFitExponential->getIntersect(), |
2037
|
|
|
$bestFitExponential->getIntersectSE(), |
2038
|
|
|
$bestFitExponential->getStdevOfResiduals(), |
2039
|
|
|
$bestFitExponential->getDFResiduals(), |
2040
|
|
|
$bestFitExponential->getSSResiduals(), |
2041
|
|
|
], |
2042
|
|
|
]; |
2043
|
|
|
} |
2044
|
|
|
|
2045
|
|
|
return [ |
2046
|
|
|
$bestFitExponential->getSlope(), |
2047
|
|
|
$bestFitExponential->getIntersect(), |
2048
|
|
|
]; |
2049
|
|
|
} |
2050
|
|
|
|
2051
|
|
|
/** |
2052
|
|
|
* LOGINV. |
2053
|
|
|
* |
2054
|
|
|
* Returns the inverse of the normal cumulative distribution |
2055
|
|
|
* |
2056
|
|
|
* @param float $probability |
2057
|
|
|
* @param float $mean |
2058
|
|
|
* @param float $stdDev |
2059
|
|
|
* |
2060
|
|
|
* @return float |
2061
|
|
|
* |
2062
|
|
|
* @todo Try implementing P J Acklam's refinement algorithm for greater |
2063
|
|
|
* accuracy if I can get my head round the mathematics |
2064
|
|
|
* (as described at) http://home.online.no/~pjacklam/notes/invnorm/ |
2065
|
|
|
*/ |
2066
|
|
|
public static function LOGINV($probability, $mean, $stdDev) |
2067
|
|
|
{ |
2068
|
|
|
$probability = Functions::flattenSingleValue($probability); |
2069
|
|
|
$mean = Functions::flattenSingleValue($mean); |
2070
|
|
|
$stdDev = Functions::flattenSingleValue($stdDev); |
2071
|
|
|
|
2072
|
|
|
if ((is_numeric($probability)) && (is_numeric($mean)) && (is_numeric($stdDev))) { |
2073
|
|
|
if (($probability < 0) || ($probability > 1) || ($stdDev <= 0)) { |
2074
|
|
|
return Functions::NAN(); |
|
|
|
|
2075
|
|
|
} |
2076
|
|
|
|
2077
|
|
|
return exp($mean + $stdDev * self::NORMSINV($probability)); |
2078
|
|
|
} |
2079
|
|
|
|
2080
|
|
|
return Functions::VALUE(); |
|
|
|
|
2081
|
|
|
} |
2082
|
|
|
|
2083
|
|
|
/** |
2084
|
|
|
* LOGNORMDIST. |
2085
|
|
|
* |
2086
|
|
|
* Returns the cumulative lognormal distribution of x, where ln(x) is normally distributed |
2087
|
|
|
* with parameters mean and standard_dev. |
2088
|
|
|
* |
2089
|
|
|
* @param float $value |
2090
|
|
|
* @param float $mean |
2091
|
|
|
* @param float $stdDev |
2092
|
|
|
* |
2093
|
|
|
* @return float |
2094
|
|
|
*/ |
2095
|
|
|
public static function LOGNORMDIST($value, $mean, $stdDev) |
2096
|
|
|
{ |
2097
|
|
|
$value = Functions::flattenSingleValue($value); |
2098
|
|
|
$mean = Functions::flattenSingleValue($mean); |
2099
|
|
|
$stdDev = Functions::flattenSingleValue($stdDev); |
2100
|
|
|
|
2101
|
|
|
if ((is_numeric($value)) && (is_numeric($mean)) && (is_numeric($stdDev))) { |
2102
|
|
|
if (($value <= 0) || ($stdDev <= 0)) { |
2103
|
|
|
return Functions::NAN(); |
|
|
|
|
2104
|
|
|
} |
2105
|
|
|
|
2106
|
|
|
return self::NORMSDIST((log($value) - $mean) / $stdDev); |
2107
|
|
|
} |
2108
|
|
|
|
2109
|
|
|
return Functions::VALUE(); |
|
|
|
|
2110
|
|
|
} |
2111
|
|
|
|
2112
|
|
|
/** |
2113
|
|
|
* MAX. |
2114
|
|
|
* |
2115
|
|
|
* MAX returns the value of the element of the values passed that has the highest value, |
2116
|
|
|
* with negative numbers considered smaller than positive numbers. |
2117
|
|
|
* |
2118
|
|
|
* Excel Function: |
2119
|
|
|
* MAX(value1[,value2[, ...]]) |
2120
|
|
|
* |
2121
|
|
|
* @category Statistical Functions |
2122
|
|
|
* |
2123
|
|
|
* @param mixed ...$args Data values |
2124
|
|
|
* |
2125
|
|
|
* @return float |
2126
|
|
|
*/ |
2127
|
5 |
|
public static function MAX(...$args) |
2128
|
|
|
{ |
2129
|
5 |
|
$returnValue = null; |
2130
|
|
|
|
2131
|
|
|
// Loop through arguments |
2132
|
5 |
|
$aArgs = Functions::flattenArray($args); |
2133
|
5 |
|
foreach ($aArgs as $arg) { |
2134
|
|
|
// Is it a numeric value? |
2135
|
5 |
|
if ((is_numeric($arg)) && (!is_string($arg))) { |
2136
|
5 |
|
if (($returnValue === null) || ($arg > $returnValue)) { |
2137
|
5 |
|
$returnValue = $arg; |
2138
|
|
|
} |
2139
|
|
|
} |
2140
|
|
|
} |
2141
|
|
|
|
2142
|
5 |
|
if ($returnValue === null) { |
2143
|
|
|
return 0; |
2144
|
|
|
} |
2145
|
|
|
|
2146
|
5 |
|
return $returnValue; |
2147
|
|
|
} |
2148
|
|
|
|
2149
|
|
|
/** |
2150
|
|
|
* MAXA. |
2151
|
|
|
* |
2152
|
|
|
* Returns the greatest value in a list of arguments, including numbers, text, and logical values |
2153
|
|
|
* |
2154
|
|
|
* Excel Function: |
2155
|
|
|
* MAXA(value1[,value2[, ...]]) |
2156
|
|
|
* |
2157
|
|
|
* @category Statistical Functions |
2158
|
|
|
* |
2159
|
|
|
* @param mixed ...$args Data values |
2160
|
|
|
* |
2161
|
|
|
* @return float |
2162
|
|
|
*/ |
2163
|
1 |
|
public static function MAXA(...$args) |
2164
|
|
|
{ |
2165
|
1 |
|
$returnValue = null; |
2166
|
|
|
|
2167
|
|
|
// Loop through arguments |
2168
|
1 |
|
$aArgs = Functions::flattenArray($args); |
2169
|
1 |
|
foreach ($aArgs as $arg) { |
2170
|
|
|
// Is it a numeric value? |
2171
|
1 |
|
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) && ($arg != '')))) { |
2172
|
1 |
|
if (is_bool($arg)) { |
2173
|
1 |
|
$arg = (int) $arg; |
2174
|
1 |
|
} elseif (is_string($arg)) { |
2175
|
1 |
|
$arg = 0; |
2176
|
|
|
} |
2177
|
1 |
|
if (($returnValue === null) || ($arg > $returnValue)) { |
2178
|
1 |
|
$returnValue = $arg; |
2179
|
|
|
} |
2180
|
|
|
} |
2181
|
|
|
} |
2182
|
|
|
|
2183
|
1 |
|
if ($returnValue === null) { |
2184
|
|
|
return 0; |
2185
|
|
|
} |
2186
|
|
|
|
2187
|
1 |
|
return $returnValue; |
2188
|
|
|
} |
2189
|
|
|
|
2190
|
|
|
/** |
2191
|
|
|
* MAXIFS. |
2192
|
|
|
* |
2193
|
|
|
* Counts the maximum value within a range of cells that contain numbers within the list of arguments |
2194
|
|
|
* |
2195
|
|
|
* Excel Function: |
2196
|
|
|
* MAXIFS(max_range, criteria_range1, criteria1, [criteria_range2, criteria2], ...) |
2197
|
|
|
* |
2198
|
|
|
* @category Statistical Functions |
2199
|
|
|
* |
2200
|
|
|
* @param mixed $args Data range and criterias |
2201
|
|
|
* |
2202
|
|
|
* @return float |
2203
|
|
|
*/ |
2204
|
2 |
|
public static function MAXIFS(...$args) |
2205
|
|
|
{ |
2206
|
2 |
|
$arrayList = $args; |
2207
|
|
|
|
2208
|
|
|
// Return value |
2209
|
2 |
|
$returnValue = null; |
2210
|
|
|
|
2211
|
2 |
|
$maxArgs = Functions::flattenArray(array_shift($arrayList)); |
2212
|
2 |
|
$aArgsArray = []; |
2213
|
2 |
|
$conditions = []; |
2214
|
|
|
|
2215
|
2 |
|
while (count($arrayList) > 0) { |
2216
|
2 |
|
$aArgsArray[] = Functions::flattenArray(array_shift($arrayList)); |
2217
|
2 |
|
$conditions[] = Functions::ifCondition(array_shift($arrayList)); |
2218
|
|
|
} |
2219
|
|
|
|
2220
|
|
|
// Loop through each arg and see if arguments and conditions are true |
2221
|
2 |
|
foreach ($maxArgs as $index => $value) { |
2222
|
2 |
|
$valid = true; |
2223
|
|
|
|
2224
|
2 |
|
foreach ($conditions as $cidx => $condition) { |
2225
|
2 |
|
$arg = $aArgsArray[$cidx][$index]; |
2226
|
|
|
|
2227
|
|
|
// Loop through arguments |
2228
|
2 |
|
if (!is_numeric($arg)) { |
2229
|
2 |
|
$arg = Calculation::wrapResult(strtoupper($arg)); |
2230
|
|
|
} |
2231
|
2 |
|
$testCondition = '=' . $arg . $condition; |
2232
|
2 |
|
if (!Calculation::getInstance()->_calculateFormulaValue($testCondition)) { |
2233
|
|
|
// Is not a value within our criteria |
2234
|
2 |
|
$valid = false; |
2235
|
|
|
|
2236
|
2 |
|
break; // if false found, don't need to check other conditions |
2237
|
|
|
} |
2238
|
|
|
} |
2239
|
|
|
|
2240
|
2 |
|
if ($valid) { |
2241
|
2 |
|
$returnValue = $returnValue === null ? $value : max($value, $returnValue); |
2242
|
|
|
} |
2243
|
|
|
} |
2244
|
|
|
|
2245
|
|
|
// Return |
2246
|
2 |
|
return $returnValue; |
2247
|
|
|
} |
2248
|
|
|
|
2249
|
|
|
/** |
2250
|
|
|
* MEDIAN. |
2251
|
|
|
* |
2252
|
|
|
* Returns the median of the given numbers. The median is the number in the middle of a set of numbers. |
2253
|
|
|
* |
2254
|
|
|
* Excel Function: |
2255
|
|
|
* MEDIAN(value1[,value2[, ...]]) |
2256
|
|
|
* |
2257
|
|
|
* @category Statistical Functions |
2258
|
|
|
* |
2259
|
|
|
* @param mixed ...$args Data values |
2260
|
|
|
* |
2261
|
|
|
* @return float |
2262
|
|
|
*/ |
2263
|
1 |
|
public static function MEDIAN(...$args) |
2264
|
|
|
{ |
2265
|
1 |
|
$returnValue = Functions::NAN(); |
2266
|
|
|
|
2267
|
1 |
|
$mArgs = []; |
2268
|
|
|
// Loop through arguments |
2269
|
1 |
|
$aArgs = Functions::flattenArray($args); |
2270
|
1 |
|
foreach ($aArgs as $arg) { |
2271
|
|
|
// Is it a numeric value? |
2272
|
1 |
|
if ((is_numeric($arg)) && (!is_string($arg))) { |
2273
|
1 |
|
$mArgs[] = $arg; |
2274
|
|
|
} |
2275
|
|
|
} |
2276
|
|
|
|
2277
|
1 |
|
$mValueCount = count($mArgs); |
2278
|
1 |
|
if ($mValueCount > 0) { |
2279
|
1 |
|
sort($mArgs, SORT_NUMERIC); |
2280
|
1 |
|
$mValueCount = $mValueCount / 2; |
2281
|
1 |
|
if ($mValueCount == floor($mValueCount)) { |
2282
|
1 |
|
$returnValue = ($mArgs[$mValueCount--] + $mArgs[$mValueCount]) / 2; |
2283
|
|
|
} else { |
2284
|
1 |
|
$mValueCount = floor($mValueCount); |
2285
|
1 |
|
$returnValue = $mArgs[$mValueCount]; |
2286
|
|
|
} |
2287
|
|
|
} |
2288
|
|
|
|
2289
|
1 |
|
return $returnValue; |
2290
|
|
|
} |
2291
|
|
|
|
2292
|
|
|
/** |
2293
|
|
|
* MIN. |
2294
|
|
|
* |
2295
|
|
|
* MIN returns the value of the element of the values passed that has the smallest value, |
2296
|
|
|
* with negative numbers considered smaller than positive numbers. |
2297
|
|
|
* |
2298
|
|
|
* Excel Function: |
2299
|
|
|
* MIN(value1[,value2[, ...]]) |
2300
|
|
|
* |
2301
|
|
|
* @category Statistical Functions |
2302
|
|
|
* |
2303
|
|
|
* @param mixed ...$args Data values |
2304
|
|
|
* |
2305
|
|
|
* @return float |
2306
|
|
|
*/ |
2307
|
5 |
|
public static function MIN(...$args) |
2308
|
|
|
{ |
2309
|
5 |
|
$returnValue = null; |
2310
|
|
|
|
2311
|
|
|
// Loop through arguments |
2312
|
5 |
|
$aArgs = Functions::flattenArray($args); |
2313
|
5 |
|
foreach ($aArgs as $arg) { |
2314
|
|
|
// Is it a numeric value? |
2315
|
5 |
|
if ((is_numeric($arg)) && (!is_string($arg))) { |
2316
|
5 |
|
if (($returnValue === null) || ($arg < $returnValue)) { |
2317
|
5 |
|
$returnValue = $arg; |
2318
|
|
|
} |
2319
|
|
|
} |
2320
|
|
|
} |
2321
|
|
|
|
2322
|
5 |
|
if ($returnValue === null) { |
2323
|
|
|
return 0; |
2324
|
|
|
} |
2325
|
|
|
|
2326
|
5 |
|
return $returnValue; |
2327
|
|
|
} |
2328
|
|
|
|
2329
|
|
|
/** |
2330
|
|
|
* MINA. |
2331
|
|
|
* |
2332
|
|
|
* Returns the smallest value in a list of arguments, including numbers, text, and logical values |
2333
|
|
|
* |
2334
|
|
|
* Excel Function: |
2335
|
|
|
* MINA(value1[,value2[, ...]]) |
2336
|
|
|
* |
2337
|
|
|
* @category Statistical Functions |
2338
|
|
|
* |
2339
|
|
|
* @param mixed ...$args Data values |
2340
|
|
|
* |
2341
|
|
|
* @return float |
2342
|
|
|
*/ |
2343
|
1 |
|
public static function MINA(...$args) |
2344
|
|
|
{ |
2345
|
1 |
|
$returnValue = null; |
2346
|
|
|
|
2347
|
|
|
// Loop through arguments |
2348
|
1 |
|
$aArgs = Functions::flattenArray($args); |
2349
|
1 |
|
foreach ($aArgs as $arg) { |
2350
|
|
|
// Is it a numeric value? |
2351
|
1 |
|
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) && ($arg != '')))) { |
2352
|
1 |
|
if (is_bool($arg)) { |
2353
|
1 |
|
$arg = (int) $arg; |
2354
|
1 |
|
} elseif (is_string($arg)) { |
2355
|
1 |
|
$arg = 0; |
2356
|
|
|
} |
2357
|
1 |
|
if (($returnValue === null) || ($arg < $returnValue)) { |
2358
|
1 |
|
$returnValue = $arg; |
2359
|
|
|
} |
2360
|
|
|
} |
2361
|
|
|
} |
2362
|
|
|
|
2363
|
1 |
|
if ($returnValue === null) { |
2364
|
|
|
return 0; |
2365
|
|
|
} |
2366
|
|
|
|
2367
|
1 |
|
return $returnValue; |
2368
|
|
|
} |
2369
|
|
|
|
2370
|
|
|
/** |
2371
|
|
|
* MINIFS. |
2372
|
|
|
* |
2373
|
|
|
* Returns the minimum value within a range of cells that contain numbers within the list of arguments |
2374
|
|
|
* |
2375
|
|
|
* Excel Function: |
2376
|
|
|
* MINIFS(min_range, criteria_range1, criteria1, [criteria_range2, criteria2], ...) |
2377
|
|
|
* |
2378
|
|
|
* @category Statistical Functions |
2379
|
|
|
* |
2380
|
|
|
* @param mixed $args Data range and criterias |
2381
|
|
|
* |
2382
|
|
|
* @return float |
2383
|
|
|
*/ |
2384
|
2 |
|
public static function MINIFS(...$args) |
2385
|
|
|
{ |
2386
|
2 |
|
$arrayList = $args; |
2387
|
|
|
|
2388
|
|
|
// Return value |
2389
|
2 |
|
$returnValue = null; |
2390
|
|
|
|
2391
|
2 |
|
$minArgs = Functions::flattenArray(array_shift($arrayList)); |
2392
|
2 |
|
$aArgsArray = []; |
2393
|
2 |
|
$conditions = []; |
2394
|
|
|
|
2395
|
2 |
|
while (count($arrayList) > 0) { |
2396
|
2 |
|
$aArgsArray[] = Functions::flattenArray(array_shift($arrayList)); |
2397
|
2 |
|
$conditions[] = Functions::ifCondition(array_shift($arrayList)); |
2398
|
|
|
} |
2399
|
|
|
|
2400
|
|
|
// Loop through each arg and see if arguments and conditions are true |
2401
|
2 |
|
foreach ($minArgs as $index => $value) { |
2402
|
2 |
|
$valid = true; |
2403
|
|
|
|
2404
|
2 |
|
foreach ($conditions as $cidx => $condition) { |
2405
|
2 |
|
$arg = $aArgsArray[$cidx][$index]; |
2406
|
|
|
|
2407
|
|
|
// Loop through arguments |
2408
|
2 |
|
if (!is_numeric($arg)) { |
2409
|
2 |
|
$arg = Calculation::wrapResult(strtoupper($arg)); |
2410
|
|
|
} |
2411
|
2 |
|
$testCondition = '=' . $arg . $condition; |
2412
|
2 |
|
if (!Calculation::getInstance()->_calculateFormulaValue($testCondition)) { |
2413
|
|
|
// Is not a value within our criteria |
2414
|
2 |
|
$valid = false; |
2415
|
|
|
|
2416
|
2 |
|
break; // if false found, don't need to check other conditions |
2417
|
|
|
} |
2418
|
|
|
} |
2419
|
|
|
|
2420
|
2 |
|
if ($valid) { |
2421
|
2 |
|
$returnValue = $returnValue === null ? $value : min($value, $returnValue); |
2422
|
|
|
} |
2423
|
|
|
} |
2424
|
|
|
|
2425
|
|
|
// Return |
2426
|
2 |
|
return $returnValue; |
2427
|
|
|
} |
2428
|
|
|
|
2429
|
|
|
// |
2430
|
|
|
// Special variant of array_count_values that isn't limited to strings and integers, |
2431
|
|
|
// but can work with floating point numbers as values |
2432
|
|
|
// |
2433
|
1 |
|
private static function modeCalc($data) |
2434
|
|
|
{ |
2435
|
1 |
|
$frequencyArray = []; |
2436
|
1 |
|
foreach ($data as $datum) { |
2437
|
1 |
|
$found = false; |
2438
|
1 |
|
foreach ($frequencyArray as $key => $value) { |
2439
|
1 |
|
if ((string) $value['value'] == (string) $datum) { |
2440
|
1 |
|
++$frequencyArray[$key]['frequency']; |
2441
|
1 |
|
$found = true; |
2442
|
|
|
|
2443
|
1 |
|
break; |
2444
|
|
|
} |
2445
|
|
|
} |
2446
|
1 |
|
if (!$found) { |
2447
|
1 |
|
$frequencyArray[] = [ |
2448
|
1 |
|
'value' => $datum, |
2449
|
1 |
|
'frequency' => 1, |
2450
|
|
|
]; |
2451
|
|
|
} |
2452
|
|
|
} |
2453
|
|
|
|
2454
|
1 |
|
foreach ($frequencyArray as $key => $value) { |
2455
|
1 |
|
$frequencyList[$key] = $value['frequency']; |
2456
|
1 |
|
$valueList[$key] = $value['value']; |
2457
|
|
|
} |
2458
|
1 |
|
array_multisort($frequencyList, SORT_DESC, $valueList, SORT_ASC, SORT_NUMERIC, $frequencyArray); |
|
|
|
|
2459
|
|
|
|
2460
|
1 |
|
if ($frequencyArray[0]['frequency'] == 1) { |
2461
|
1 |
|
return Functions::NA(); |
2462
|
|
|
} |
2463
|
|
|
|
2464
|
1 |
|
return $frequencyArray[0]['value']; |
2465
|
|
|
} |
2466
|
|
|
|
2467
|
|
|
/** |
2468
|
|
|
* MODE. |
2469
|
|
|
* |
2470
|
|
|
* Returns the most frequently occurring, or repetitive, value in an array or range of data |
2471
|
|
|
* |
2472
|
|
|
* Excel Function: |
2473
|
|
|
* MODE(value1[,value2[, ...]]) |
2474
|
|
|
* |
2475
|
|
|
* @category Statistical Functions |
2476
|
|
|
* |
2477
|
|
|
* @param mixed ...$args Data values |
2478
|
|
|
* |
2479
|
|
|
* @return float |
2480
|
|
|
*/ |
2481
|
1 |
|
public static function MODE(...$args) |
2482
|
|
|
{ |
2483
|
1 |
|
$returnValue = Functions::NA(); |
2484
|
|
|
|
2485
|
|
|
// Loop through arguments |
2486
|
1 |
|
$aArgs = Functions::flattenArray($args); |
2487
|
|
|
|
2488
|
1 |
|
$mArgs = []; |
2489
|
1 |
|
foreach ($aArgs as $arg) { |
2490
|
|
|
// Is it a numeric value? |
2491
|
1 |
|
if ((is_numeric($arg)) && (!is_string($arg))) { |
2492
|
1 |
|
$mArgs[] = $arg; |
2493
|
|
|
} |
2494
|
|
|
} |
2495
|
|
|
|
2496
|
1 |
|
if (!empty($mArgs)) { |
2497
|
1 |
|
return self::modeCalc($mArgs); |
|
|
|
|
2498
|
|
|
} |
2499
|
|
|
|
2500
|
|
|
return $returnValue; |
|
|
|
|
2501
|
|
|
} |
2502
|
|
|
|
2503
|
|
|
/** |
2504
|
|
|
* NEGBINOMDIST. |
2505
|
|
|
* |
2506
|
|
|
* Returns the negative binomial distribution. NEGBINOMDIST returns the probability that |
2507
|
|
|
* there will be number_f failures before the number_s-th success, when the constant |
2508
|
|
|
* probability of a success is probability_s. This function is similar to the binomial |
2509
|
|
|
* distribution, except that the number of successes is fixed, and the number of trials is |
2510
|
|
|
* variable. Like the binomial, trials are assumed to be independent. |
2511
|
|
|
* |
2512
|
|
|
* @param float $failures Number of Failures |
2513
|
|
|
* @param float $successes Threshold number of Successes |
2514
|
|
|
* @param float $probability Probability of success on each trial |
2515
|
|
|
* |
2516
|
|
|
* @return float |
2517
|
|
|
*/ |
2518
|
|
|
public static function NEGBINOMDIST($failures, $successes, $probability) |
2519
|
|
|
{ |
2520
|
|
|
$failures = floor(Functions::flattenSingleValue($failures)); |
2521
|
|
|
$successes = floor(Functions::flattenSingleValue($successes)); |
2522
|
|
|
$probability = Functions::flattenSingleValue($probability); |
2523
|
|
|
|
2524
|
|
|
if ((is_numeric($failures)) && (is_numeric($successes)) && (is_numeric($probability))) { |
|
|
|
|
2525
|
|
|
if (($failures < 0) || ($successes < 1)) { |
2526
|
|
|
return Functions::NAN(); |
|
|
|
|
2527
|
|
|
} elseif (($probability < 0) || ($probability > 1)) { |
2528
|
|
|
return Functions::NAN(); |
|
|
|
|
2529
|
|
|
} |
2530
|
|
|
if (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_GNUMERIC) { |
2531
|
|
|
if (($failures + $successes - 1) <= 0) { |
2532
|
|
|
return Functions::NAN(); |
|
|
|
|
2533
|
|
|
} |
2534
|
|
|
} |
2535
|
|
|
|
2536
|
|
|
return (MathTrig::COMBIN($failures + $successes - 1, $successes - 1)) * (pow($probability, $successes)) * (pow(1 - $probability, $failures)); |
|
|
|
|
2537
|
|
|
} |
2538
|
|
|
|
2539
|
|
|
return Functions::VALUE(); |
|
|
|
|
2540
|
|
|
} |
2541
|
|
|
|
2542
|
|
|
/** |
2543
|
|
|
* NORMDIST. |
2544
|
|
|
* |
2545
|
|
|
* Returns the normal distribution for the specified mean and standard deviation. This |
2546
|
|
|
* function has a very wide range of applications in statistics, including hypothesis |
2547
|
|
|
* testing. |
2548
|
|
|
* |
2549
|
|
|
* @param float $value |
2550
|
|
|
* @param float $mean Mean Value |
2551
|
|
|
* @param float $stdDev Standard Deviation |
2552
|
|
|
* @param bool $cumulative |
2553
|
|
|
* |
2554
|
|
|
* @return float |
2555
|
|
|
*/ |
2556
|
|
|
public static function NORMDIST($value, $mean, $stdDev, $cumulative) |
2557
|
|
|
{ |
2558
|
|
|
$value = Functions::flattenSingleValue($value); |
2559
|
|
|
$mean = Functions::flattenSingleValue($mean); |
2560
|
|
|
$stdDev = Functions::flattenSingleValue($stdDev); |
2561
|
|
|
|
2562
|
|
|
if ((is_numeric($value)) && (is_numeric($mean)) && (is_numeric($stdDev))) { |
2563
|
|
|
if ($stdDev < 0) { |
2564
|
|
|
return Functions::NAN(); |
|
|
|
|
2565
|
|
|
} |
2566
|
|
|
if ((is_numeric($cumulative)) || (is_bool($cumulative))) { |
|
|
|
|
2567
|
|
|
if ($cumulative) { |
2568
|
|
|
return 0.5 * (1 + Engineering::erfVal(($value - $mean) / ($stdDev * sqrt(2)))); |
2569
|
|
|
} |
2570
|
|
|
|
2571
|
|
|
return (1 / (self::SQRT2PI * $stdDev)) * exp(0 - (pow($value - $mean, 2) / (2 * ($stdDev * $stdDev)))); |
2572
|
|
|
} |
2573
|
|
|
} |
2574
|
|
|
|
2575
|
|
|
return Functions::VALUE(); |
|
|
|
|
2576
|
|
|
} |
2577
|
|
|
|
2578
|
|
|
/** |
2579
|
|
|
* NORMINV. |
2580
|
|
|
* |
2581
|
|
|
* Returns the inverse of the normal cumulative distribution for the specified mean and standard deviation. |
2582
|
|
|
* |
2583
|
|
|
* @param float $probability |
2584
|
|
|
* @param float $mean Mean Value |
2585
|
|
|
* @param float $stdDev Standard Deviation |
2586
|
|
|
* |
2587
|
|
|
* @return float |
2588
|
|
|
*/ |
2589
|
|
|
public static function NORMINV($probability, $mean, $stdDev) |
2590
|
|
|
{ |
2591
|
|
|
$probability = Functions::flattenSingleValue($probability); |
2592
|
|
|
$mean = Functions::flattenSingleValue($mean); |
2593
|
|
|
$stdDev = Functions::flattenSingleValue($stdDev); |
2594
|
|
|
|
2595
|
|
|
if ((is_numeric($probability)) && (is_numeric($mean)) && (is_numeric($stdDev))) { |
2596
|
|
|
if (($probability < 0) || ($probability > 1)) { |
2597
|
|
|
return Functions::NAN(); |
|
|
|
|
2598
|
|
|
} |
2599
|
|
|
if ($stdDev < 0) { |
2600
|
|
|
return Functions::NAN(); |
|
|
|
|
2601
|
|
|
} |
2602
|
|
|
|
2603
|
|
|
return (self::inverseNcdf($probability) * $stdDev) + $mean; |
2604
|
|
|
} |
2605
|
|
|
|
2606
|
|
|
return Functions::VALUE(); |
|
|
|
|
2607
|
|
|
} |
2608
|
|
|
|
2609
|
|
|
/** |
2610
|
|
|
* NORMSDIST. |
2611
|
|
|
* |
2612
|
|
|
* Returns the standard normal cumulative distribution function. The distribution has |
2613
|
|
|
* a mean of 0 (zero) and a standard deviation of one. Use this function in place of a |
2614
|
|
|
* table of standard normal curve areas. |
2615
|
|
|
* |
2616
|
|
|
* @param float $value |
2617
|
|
|
* |
2618
|
|
|
* @return float |
2619
|
|
|
*/ |
2620
|
|
|
public static function NORMSDIST($value) |
2621
|
|
|
{ |
2622
|
|
|
$value = Functions::flattenSingleValue($value); |
2623
|
|
|
|
2624
|
|
|
return self::NORMDIST($value, 0, 1, true); |
2625
|
|
|
} |
2626
|
|
|
|
2627
|
|
|
/** |
2628
|
|
|
* NORMSINV. |
2629
|
|
|
* |
2630
|
|
|
* Returns the inverse of the standard normal cumulative distribution |
2631
|
|
|
* |
2632
|
|
|
* @param float $value |
2633
|
|
|
* |
2634
|
|
|
* @return float |
2635
|
|
|
*/ |
2636
|
|
|
public static function NORMSINV($value) |
2637
|
|
|
{ |
2638
|
|
|
return self::NORMINV($value, 0, 1); |
2639
|
|
|
} |
2640
|
|
|
|
2641
|
|
|
/** |
2642
|
|
|
* PERCENTILE. |
2643
|
|
|
* |
2644
|
|
|
* Returns the nth percentile of values in a range.. |
2645
|
|
|
* |
2646
|
|
|
* Excel Function: |
2647
|
|
|
* PERCENTILE(value1[,value2[, ...]],entry) |
2648
|
|
|
* |
2649
|
|
|
* @category Statistical Functions |
2650
|
|
|
* |
2651
|
|
|
* @param mixed $args Data values |
2652
|
|
|
* @param float $entry Percentile value in the range 0..1, inclusive. |
2653
|
|
|
* |
2654
|
|
|
* @return float |
2655
|
|
|
*/ |
2656
|
|
|
public static function PERCENTILE(...$args) |
2657
|
|
|
{ |
2658
|
|
|
$aArgs = Functions::flattenArray($args); |
2659
|
|
|
|
2660
|
|
|
// Calculate |
2661
|
|
|
$entry = array_pop($aArgs); |
2662
|
|
|
|
2663
|
|
|
if ((is_numeric($entry)) && (!is_string($entry))) { |
2664
|
|
|
if (($entry < 0) || ($entry > 1)) { |
2665
|
|
|
return Functions::NAN(); |
|
|
|
|
2666
|
|
|
} |
2667
|
|
|
$mArgs = []; |
2668
|
|
|
foreach ($aArgs as $arg) { |
2669
|
|
|
// Is it a numeric value? |
2670
|
|
|
if ((is_numeric($arg)) && (!is_string($arg))) { |
2671
|
|
|
$mArgs[] = $arg; |
2672
|
|
|
} |
2673
|
|
|
} |
2674
|
|
|
$mValueCount = count($mArgs); |
2675
|
|
|
if ($mValueCount > 0) { |
2676
|
|
|
sort($mArgs); |
2677
|
|
|
$count = self::COUNT($mArgs); |
2678
|
|
|
$index = $entry * ($count - 1); |
2679
|
|
|
$iBase = floor($index); |
2680
|
|
|
if ($index == $iBase) { |
2681
|
|
|
return $mArgs[$index]; |
2682
|
|
|
} |
2683
|
|
|
$iNext = $iBase + 1; |
2684
|
|
|
$iProportion = $index - $iBase; |
2685
|
|
|
|
2686
|
|
|
return $mArgs[$iBase] + (($mArgs[$iNext] - $mArgs[$iBase]) * $iProportion); |
2687
|
|
|
} |
2688
|
|
|
} |
2689
|
|
|
|
2690
|
|
|
return Functions::VALUE(); |
|
|
|
|
2691
|
|
|
} |
2692
|
|
|
|
2693
|
|
|
/** |
2694
|
|
|
* PERCENTRANK. |
2695
|
|
|
* |
2696
|
|
|
* Returns the rank of a value in a data set as a percentage of the data set. |
2697
|
|
|
* |
2698
|
|
|
* @param float[] $valueSet An array of, or a reference to, a list of numbers |
2699
|
|
|
* @param int $value the number whose rank you want to find |
2700
|
|
|
* @param int $significance the number of significant digits for the returned percentage value |
2701
|
|
|
* |
2702
|
|
|
* @return float |
2703
|
|
|
*/ |
2704
|
|
|
public static function PERCENTRANK($valueSet, $value, $significance = 3) |
2705
|
|
|
{ |
2706
|
|
|
$valueSet = Functions::flattenArray($valueSet); |
2707
|
|
|
$value = Functions::flattenSingleValue($value); |
2708
|
|
|
$significance = ($significance === null) ? 3 : (int) Functions::flattenSingleValue($significance); |
|
|
|
|
2709
|
|
|
|
2710
|
|
|
foreach ($valueSet as $key => $valueEntry) { |
2711
|
|
|
if (!is_numeric($valueEntry)) { |
2712
|
|
|
unset($valueSet[$key]); |
2713
|
|
|
} |
2714
|
|
|
} |
2715
|
|
|
sort($valueSet, SORT_NUMERIC); |
2716
|
|
|
$valueCount = count($valueSet); |
2717
|
|
|
if ($valueCount == 0) { |
2718
|
|
|
return Functions::NAN(); |
|
|
|
|
2719
|
|
|
} |
2720
|
|
|
|
2721
|
|
|
$valueAdjustor = $valueCount - 1; |
2722
|
|
|
if (($value < $valueSet[0]) || ($value > $valueSet[$valueAdjustor])) { |
2723
|
|
|
return Functions::NA(); |
|
|
|
|
2724
|
|
|
} |
2725
|
|
|
|
2726
|
|
|
$pos = array_search($value, $valueSet); |
2727
|
|
|
if ($pos === false) { |
2728
|
|
|
$pos = 0; |
2729
|
|
|
$testValue = $valueSet[0]; |
2730
|
|
|
while ($testValue < $value) { |
2731
|
|
|
$testValue = $valueSet[++$pos]; |
2732
|
|
|
} |
2733
|
|
|
--$pos; |
2734
|
|
|
$pos += (($value - $valueSet[$pos]) / ($testValue - $valueSet[$pos])); |
2735
|
|
|
} |
2736
|
|
|
|
2737
|
|
|
return round($pos / $valueAdjustor, $significance); |
2738
|
|
|
} |
2739
|
|
|
|
2740
|
|
|
/** |
2741
|
|
|
* PERMUT. |
2742
|
|
|
* |
2743
|
|
|
* Returns the number of permutations for a given number of objects that can be |
2744
|
|
|
* selected from number objects. A permutation is any set or subset of objects or |
2745
|
|
|
* events where internal order is significant. Permutations are different from |
2746
|
|
|
* combinations, for which the internal order is not significant. Use this function |
2747
|
|
|
* for lottery-style probability calculations. |
2748
|
|
|
* |
2749
|
|
|
* @param int $numObjs Number of different objects |
2750
|
|
|
* @param int $numInSet Number of objects in each permutation |
2751
|
|
|
* |
2752
|
|
|
* @return int Number of permutations |
2753
|
|
|
*/ |
2754
|
|
|
public static function PERMUT($numObjs, $numInSet) |
2755
|
|
|
{ |
2756
|
|
|
$numObjs = Functions::flattenSingleValue($numObjs); |
2757
|
|
|
$numInSet = Functions::flattenSingleValue($numInSet); |
2758
|
|
|
|
2759
|
|
|
if ((is_numeric($numObjs)) && (is_numeric($numInSet))) { |
2760
|
|
|
$numInSet = floor($numInSet); |
2761
|
|
|
if ($numObjs < $numInSet) { |
2762
|
|
|
return Functions::NAN(); |
|
|
|
|
2763
|
|
|
} |
2764
|
|
|
|
2765
|
|
|
return round(MathTrig::FACT($numObjs) / MathTrig::FACT($numObjs - $numInSet)); |
2766
|
|
|
} |
2767
|
|
|
|
2768
|
|
|
return Functions::VALUE(); |
|
|
|
|
2769
|
|
|
} |
2770
|
|
|
|
2771
|
|
|
/** |
2772
|
|
|
* POISSON. |
2773
|
|
|
* |
2774
|
|
|
* Returns the Poisson distribution. A common application of the Poisson distribution |
2775
|
|
|
* is predicting the number of events over a specific time, such as the number of |
2776
|
|
|
* cars arriving at a toll plaza in 1 minute. |
2777
|
|
|
* |
2778
|
|
|
* @param float $value |
2779
|
|
|
* @param float $mean Mean Value |
2780
|
|
|
* @param bool $cumulative |
2781
|
|
|
* |
2782
|
|
|
* @return float |
2783
|
|
|
*/ |
2784
|
|
|
public static function POISSON($value, $mean, $cumulative) |
2785
|
|
|
{ |
2786
|
|
|
$value = Functions::flattenSingleValue($value); |
2787
|
|
|
$mean = Functions::flattenSingleValue($mean); |
2788
|
|
|
|
2789
|
|
|
if ((is_numeric($value)) && (is_numeric($mean))) { |
2790
|
|
|
if (($value < 0) || ($mean <= 0)) { |
2791
|
|
|
return Functions::NAN(); |
|
|
|
|
2792
|
|
|
} |
2793
|
|
|
if ((is_numeric($cumulative)) || (is_bool($cumulative))) { |
|
|
|
|
2794
|
|
|
if ($cumulative) { |
2795
|
|
|
$summer = 0; |
2796
|
|
|
$floor = floor($value); |
2797
|
|
|
for ($i = 0; $i <= $floor; ++$i) { |
2798
|
|
|
$summer += pow($mean, $i) / MathTrig::FACT($i); |
2799
|
|
|
} |
2800
|
|
|
|
2801
|
|
|
return exp(0 - $mean) * $summer; |
2802
|
|
|
} |
2803
|
|
|
|
2804
|
|
|
return (exp(0 - $mean) * pow($mean, $value)) / MathTrig::FACT($value); |
2805
|
|
|
} |
2806
|
|
|
} |
2807
|
|
|
|
2808
|
|
|
return Functions::VALUE(); |
|
|
|
|
2809
|
|
|
} |
2810
|
|
|
|
2811
|
|
|
/** |
2812
|
|
|
* QUARTILE. |
2813
|
|
|
* |
2814
|
|
|
* Returns the quartile of a data set. |
2815
|
|
|
* |
2816
|
|
|
* Excel Function: |
2817
|
|
|
* QUARTILE(value1[,value2[, ...]],entry) |
2818
|
|
|
* |
2819
|
|
|
* @category Statistical Functions |
2820
|
|
|
* |
2821
|
|
|
* @param mixed $args Data values |
2822
|
|
|
* @param int $entry Quartile value in the range 1..3, inclusive. |
2823
|
|
|
* |
2824
|
|
|
* @return float |
2825
|
|
|
*/ |
2826
|
|
|
public static function QUARTILE(...$args) |
2827
|
|
|
{ |
2828
|
|
|
$aArgs = Functions::flattenArray($args); |
2829
|
|
|
|
2830
|
|
|
// Calculate |
2831
|
|
|
$entry = floor(array_pop($aArgs)); |
2832
|
|
|
|
2833
|
|
|
if ((is_numeric($entry)) && (!is_string($entry))) { |
|
|
|
|
2834
|
|
|
$entry /= 4; |
2835
|
|
|
if (($entry < 0) || ($entry > 1)) { |
2836
|
|
|
return Functions::NAN(); |
|
|
|
|
2837
|
|
|
} |
2838
|
|
|
|
2839
|
|
|
return self::PERCENTILE($aArgs, $entry); |
2840
|
|
|
} |
2841
|
|
|
|
2842
|
|
|
return Functions::VALUE(); |
2843
|
|
|
} |
2844
|
|
|
|
2845
|
|
|
/** |
2846
|
|
|
* RANK. |
2847
|
|
|
* |
2848
|
|
|
* Returns the rank of a number in a list of numbers. |
2849
|
|
|
* |
2850
|
|
|
* @param int $value the number whose rank you want to find |
2851
|
|
|
* @param float[] $valueSet An array of, or a reference to, a list of numbers |
2852
|
|
|
* @param int $order Order to sort the values in the value set |
2853
|
|
|
* |
2854
|
|
|
* @return float |
2855
|
|
|
*/ |
2856
|
|
|
public static function RANK($value, $valueSet, $order = 0) |
2857
|
|
|
{ |
2858
|
|
|
$value = Functions::flattenSingleValue($value); |
2859
|
|
|
$valueSet = Functions::flattenArray($valueSet); |
2860
|
|
|
$order = ($order === null) ? 0 : (int) Functions::flattenSingleValue($order); |
|
|
|
|
2861
|
|
|
|
2862
|
|
|
foreach ($valueSet as $key => $valueEntry) { |
2863
|
|
|
if (!is_numeric($valueEntry)) { |
2864
|
|
|
unset($valueSet[$key]); |
2865
|
|
|
} |
2866
|
|
|
} |
2867
|
|
|
|
2868
|
|
|
if ($order == 0) { |
2869
|
|
|
rsort($valueSet, SORT_NUMERIC); |
2870
|
|
|
} else { |
2871
|
|
|
sort($valueSet, SORT_NUMERIC); |
2872
|
|
|
} |
2873
|
|
|
$pos = array_search($value, $valueSet); |
2874
|
|
|
if ($pos === false) { |
2875
|
|
|
return Functions::NA(); |
|
|
|
|
2876
|
|
|
} |
2877
|
|
|
|
2878
|
|
|
return ++$pos; |
2879
|
|
|
} |
2880
|
|
|
|
2881
|
|
|
/** |
2882
|
|
|
* RSQ. |
2883
|
|
|
* |
2884
|
|
|
* Returns the square of the Pearson product moment correlation coefficient through data points in known_y's and known_x's. |
2885
|
|
|
* |
2886
|
|
|
* @param mixed[] $yValues Data Series Y |
2887
|
|
|
* @param mixed[] $xValues Data Series X |
2888
|
|
|
* |
2889
|
|
|
* @return float |
2890
|
|
|
*/ |
2891
|
|
|
public static function RSQ($yValues, $xValues) |
2892
|
|
|
{ |
2893
|
|
|
if (!self::checkTrendArrays($yValues, $xValues)) { |
2894
|
|
|
return Functions::VALUE(); |
|
|
|
|
2895
|
|
|
} |
2896
|
|
|
$yValueCount = count($yValues); |
2897
|
|
|
$xValueCount = count($xValues); |
2898
|
|
|
|
2899
|
|
|
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) { |
2900
|
|
|
return Functions::NA(); |
|
|
|
|
2901
|
|
|
} elseif ($yValueCount == 1) { |
2902
|
|
|
return Functions::DIV0(); |
|
|
|
|
2903
|
|
|
} |
2904
|
|
|
|
2905
|
|
|
$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues); |
2906
|
|
|
|
2907
|
|
|
return $bestFitLinear->getGoodnessOfFit(); |
2908
|
|
|
} |
2909
|
|
|
|
2910
|
|
|
/** |
2911
|
|
|
* SKEW. |
2912
|
|
|
* |
2913
|
|
|
* Returns the skewness of a distribution. Skewness characterizes the degree of asymmetry |
2914
|
|
|
* of a distribution around its mean. Positive skewness indicates a distribution with an |
2915
|
|
|
* asymmetric tail extending toward more positive values. Negative skewness indicates a |
2916
|
|
|
* distribution with an asymmetric tail extending toward more negative values. |
2917
|
|
|
* |
2918
|
|
|
* @param array ...$args Data Series |
2919
|
|
|
* |
2920
|
|
|
* @return float|string |
2921
|
|
|
*/ |
2922
|
|
|
public static function SKEW(...$args) |
2923
|
|
|
{ |
2924
|
|
|
$aArgs = Functions::flattenArrayIndexed($args); |
2925
|
|
|
$mean = self::AVERAGE($aArgs); |
2926
|
|
|
$stdDev = self::STDEV($aArgs); |
2927
|
|
|
|
2928
|
|
|
$count = $summer = 0; |
2929
|
|
|
// Loop through arguments |
2930
|
|
|
foreach ($aArgs as $k => $arg) { |
2931
|
|
|
if ((is_bool($arg)) && |
2932
|
|
|
(!Functions::isMatrixValue($k))) { |
2933
|
|
|
} else { |
2934
|
|
|
// Is it a numeric value? |
2935
|
|
|
if ((is_numeric($arg)) && (!is_string($arg))) { |
2936
|
|
|
$summer += pow((($arg - $mean) / $stdDev), 3); |
2937
|
|
|
++$count; |
2938
|
|
|
} |
2939
|
|
|
} |
2940
|
|
|
} |
2941
|
|
|
|
2942
|
|
|
if ($count > 2) { |
2943
|
|
|
return $summer * ($count / (($count - 1) * ($count - 2))); |
2944
|
|
|
} |
2945
|
|
|
|
2946
|
|
|
return Functions::DIV0(); |
2947
|
|
|
} |
2948
|
|
|
|
2949
|
|
|
/** |
2950
|
|
|
* SLOPE. |
2951
|
|
|
* |
2952
|
|
|
* Returns the slope of the linear regression line through data points in known_y's and known_x's. |
2953
|
|
|
* |
2954
|
|
|
* @param mixed[] $yValues Data Series Y |
2955
|
|
|
* @param mixed[] $xValues Data Series X |
2956
|
|
|
* |
2957
|
|
|
* @return float |
2958
|
|
|
*/ |
2959
|
|
|
public static function SLOPE($yValues, $xValues) |
2960
|
|
|
{ |
2961
|
|
|
if (!self::checkTrendArrays($yValues, $xValues)) { |
2962
|
|
|
return Functions::VALUE(); |
|
|
|
|
2963
|
|
|
} |
2964
|
|
|
$yValueCount = count($yValues); |
2965
|
|
|
$xValueCount = count($xValues); |
2966
|
|
|
|
2967
|
|
|
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) { |
2968
|
|
|
return Functions::NA(); |
|
|
|
|
2969
|
|
|
} elseif ($yValueCount == 1) { |
2970
|
|
|
return Functions::DIV0(); |
|
|
|
|
2971
|
|
|
} |
2972
|
|
|
|
2973
|
|
|
$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues); |
2974
|
|
|
|
2975
|
|
|
return $bestFitLinear->getSlope(); |
2976
|
|
|
} |
2977
|
|
|
|
2978
|
|
|
/** |
2979
|
|
|
* SMALL. |
2980
|
|
|
* |
2981
|
|
|
* Returns the nth smallest value in a data set. You can use this function to |
2982
|
|
|
* select a value based on its relative standing. |
2983
|
|
|
* |
2984
|
|
|
* Excel Function: |
2985
|
|
|
* SMALL(value1[,value2[, ...]],entry) |
2986
|
|
|
* |
2987
|
|
|
* @category Statistical Functions |
2988
|
|
|
* |
2989
|
|
|
* @param mixed $args Data values |
2990
|
|
|
* @param int $entry Position (ordered from the smallest) in the array or range of data to return |
2991
|
|
|
* |
2992
|
|
|
* @return float |
2993
|
|
|
*/ |
2994
|
|
|
public static function SMALL(...$args) |
2995
|
|
|
{ |
2996
|
|
|
$aArgs = Functions::flattenArray($args); |
2997
|
|
|
|
2998
|
|
|
// Calculate |
2999
|
|
|
$entry = array_pop($aArgs); |
3000
|
|
|
|
3001
|
|
|
if ((is_numeric($entry)) && (!is_string($entry))) { |
3002
|
|
|
$mArgs = []; |
3003
|
|
|
foreach ($aArgs as $arg) { |
3004
|
|
|
// Is it a numeric value? |
3005
|
|
|
if ((is_numeric($arg)) && (!is_string($arg))) { |
3006
|
|
|
$mArgs[] = $arg; |
3007
|
|
|
} |
3008
|
|
|
} |
3009
|
|
|
$count = self::COUNT($mArgs); |
3010
|
|
|
$entry = floor(--$entry); |
3011
|
|
|
if (($entry < 0) || ($entry >= $count) || ($count == 0)) { |
3012
|
|
|
return Functions::NAN(); |
|
|
|
|
3013
|
|
|
} |
3014
|
|
|
sort($mArgs); |
3015
|
|
|
|
3016
|
|
|
return $mArgs[$entry]; |
3017
|
|
|
} |
3018
|
|
|
|
3019
|
|
|
return Functions::VALUE(); |
|
|
|
|
3020
|
|
|
} |
3021
|
|
|
|
3022
|
|
|
/** |
3023
|
|
|
* STANDARDIZE. |
3024
|
|
|
* |
3025
|
|
|
* Returns a normalized value from a distribution characterized by mean and standard_dev. |
3026
|
|
|
* |
3027
|
|
|
* @param float $value Value to normalize |
3028
|
|
|
* @param float $mean Mean Value |
3029
|
|
|
* @param float $stdDev Standard Deviation |
3030
|
|
|
* |
3031
|
|
|
* @return float Standardized value |
3032
|
|
|
*/ |
3033
|
|
|
public static function STANDARDIZE($value, $mean, $stdDev) |
3034
|
|
|
{ |
3035
|
|
|
$value = Functions::flattenSingleValue($value); |
3036
|
|
|
$mean = Functions::flattenSingleValue($mean); |
3037
|
|
|
$stdDev = Functions::flattenSingleValue($stdDev); |
3038
|
|
|
|
3039
|
|
|
if ((is_numeric($value)) && (is_numeric($mean)) && (is_numeric($stdDev))) { |
3040
|
|
|
if ($stdDev <= 0) { |
3041
|
|
|
return Functions::NAN(); |
|
|
|
|
3042
|
|
|
} |
3043
|
|
|
|
3044
|
|
|
return ($value - $mean) / $stdDev; |
3045
|
|
|
} |
3046
|
|
|
|
3047
|
|
|
return Functions::VALUE(); |
|
|
|
|
3048
|
|
|
} |
3049
|
|
|
|
3050
|
|
|
/** |
3051
|
|
|
* STDEV. |
3052
|
|
|
* |
3053
|
|
|
* Estimates standard deviation based on a sample. The standard deviation is a measure of how |
3054
|
|
|
* widely values are dispersed from the average value (the mean). |
3055
|
|
|
* |
3056
|
|
|
* Excel Function: |
3057
|
|
|
* STDEV(value1[,value2[, ...]]) |
3058
|
|
|
* |
3059
|
|
|
* @category Statistical Functions |
3060
|
|
|
* |
3061
|
|
|
* @param mixed ...$args Data values |
3062
|
|
|
* |
3063
|
|
|
* @return float|string |
3064
|
|
|
*/ |
3065
|
4 |
|
public static function STDEV(...$args) |
3066
|
|
|
{ |
3067
|
4 |
|
$aArgs = Functions::flattenArrayIndexed($args); |
3068
|
|
|
|
3069
|
|
|
// Return value |
3070
|
4 |
|
$returnValue = null; |
3071
|
|
|
|
3072
|
4 |
|
$aMean = self::AVERAGE($aArgs); |
3073
|
4 |
|
if ($aMean !== null) { |
|
|
|
|
3074
|
4 |
|
$aCount = -1; |
3075
|
4 |
|
foreach ($aArgs as $k => $arg) { |
3076
|
4 |
|
if ((is_bool($arg)) && |
3077
|
4 |
|
((!Functions::isCellValue($k)) || (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE))) { |
3078
|
|
|
$arg = (int) $arg; |
3079
|
|
|
} |
3080
|
|
|
// Is it a numeric value? |
3081
|
4 |
|
if ((is_numeric($arg)) && (!is_string($arg))) { |
3082
|
4 |
|
if ($returnValue === null) { |
3083
|
4 |
|
$returnValue = pow(($arg - $aMean), 2); |
3084
|
|
|
} else { |
3085
|
4 |
|
$returnValue += pow(($arg - $aMean), 2); |
3086
|
|
|
} |
3087
|
4 |
|
++$aCount; |
3088
|
|
|
} |
3089
|
|
|
} |
3090
|
|
|
|
3091
|
|
|
// Return |
3092
|
4 |
|
if (($aCount > 0) && ($returnValue >= 0)) { |
3093
|
4 |
|
return sqrt($returnValue / $aCount); |
3094
|
|
|
} |
3095
|
|
|
} |
3096
|
|
|
|
3097
|
|
|
return Functions::DIV0(); |
3098
|
|
|
} |
3099
|
|
|
|
3100
|
|
|
/** |
3101
|
|
|
* STDEVA. |
3102
|
|
|
* |
3103
|
|
|
* Estimates standard deviation based on a sample, including numbers, text, and logical values |
3104
|
|
|
* |
3105
|
|
|
* Excel Function: |
3106
|
|
|
* STDEVA(value1[,value2[, ...]]) |
3107
|
|
|
* |
3108
|
|
|
* @category Statistical Functions |
3109
|
|
|
* |
3110
|
|
|
* @param mixed ...$args Data values |
3111
|
|
|
* |
3112
|
|
|
* @return float|string |
3113
|
|
|
*/ |
3114
|
1 |
|
public static function STDEVA(...$args) |
3115
|
|
|
{ |
3116
|
1 |
|
$aArgs = Functions::flattenArrayIndexed($args); |
3117
|
|
|
|
3118
|
1 |
|
$returnValue = null; |
3119
|
|
|
|
3120
|
1 |
|
$aMean = self::AVERAGEA($aArgs); |
3121
|
1 |
|
if ($aMean !== null) { |
|
|
|
|
3122
|
1 |
|
$aCount = -1; |
3123
|
1 |
|
foreach ($aArgs as $k => $arg) { |
3124
|
1 |
|
if ((is_bool($arg)) && |
3125
|
1 |
|
(!Functions::isMatrixValue($k))) { |
3126
|
|
|
} else { |
3127
|
|
|
// Is it a numeric value? |
3128
|
1 |
|
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) & ($arg != '')))) { |
|
|
|
|
3129
|
1 |
|
if (is_bool($arg)) { |
3130
|
1 |
|
$arg = (int) $arg; |
3131
|
1 |
|
} elseif (is_string($arg)) { |
3132
|
1 |
|
$arg = 0; |
3133
|
|
|
} |
3134
|
1 |
|
if ($returnValue === null) { |
3135
|
1 |
|
$returnValue = pow(($arg - $aMean), 2); |
3136
|
|
|
} else { |
3137
|
1 |
|
$returnValue += pow(($arg - $aMean), 2); |
3138
|
|
|
} |
3139
|
1 |
|
++$aCount; |
3140
|
|
|
} |
3141
|
|
|
} |
3142
|
|
|
} |
3143
|
|
|
|
3144
|
1 |
|
if (($aCount > 0) && ($returnValue >= 0)) { |
3145
|
1 |
|
return sqrt($returnValue / $aCount); |
3146
|
|
|
} |
3147
|
|
|
} |
3148
|
|
|
|
3149
|
|
|
return Functions::DIV0(); |
3150
|
|
|
} |
3151
|
|
|
|
3152
|
|
|
/** |
3153
|
|
|
* STDEVP. |
3154
|
|
|
* |
3155
|
|
|
* Calculates standard deviation based on the entire population |
3156
|
|
|
* |
3157
|
|
|
* Excel Function: |
3158
|
|
|
* STDEVP(value1[,value2[, ...]]) |
3159
|
|
|
* |
3160
|
|
|
* @category Statistical Functions |
3161
|
|
|
* |
3162
|
|
|
* @param mixed ...$args Data values |
3163
|
|
|
* |
3164
|
|
|
* @return float|string |
3165
|
|
|
*/ |
3166
|
4 |
|
public static function STDEVP(...$args) |
3167
|
|
|
{ |
3168
|
4 |
|
$aArgs = Functions::flattenArrayIndexed($args); |
3169
|
|
|
|
3170
|
4 |
|
$returnValue = null; |
3171
|
|
|
|
3172
|
4 |
|
$aMean = self::AVERAGE($aArgs); |
3173
|
4 |
|
if ($aMean !== null) { |
|
|
|
|
3174
|
4 |
|
$aCount = 0; |
3175
|
4 |
|
foreach ($aArgs as $k => $arg) { |
3176
|
4 |
|
if ((is_bool($arg)) && |
3177
|
4 |
|
((!Functions::isCellValue($k)) || (Functions::getCompatibilityMode() == Functions::COMPATIBILITY_OPENOFFICE))) { |
3178
|
|
|
$arg = (int) $arg; |
3179
|
|
|
} |
3180
|
|
|
// Is it a numeric value? |
3181
|
4 |
|
if ((is_numeric($arg)) && (!is_string($arg))) { |
3182
|
4 |
|
if ($returnValue === null) { |
3183
|
4 |
|
$returnValue = pow(($arg - $aMean), 2); |
3184
|
|
|
} else { |
3185
|
4 |
|
$returnValue += pow(($arg - $aMean), 2); |
3186
|
|
|
} |
3187
|
4 |
|
++$aCount; |
3188
|
|
|
} |
3189
|
|
|
} |
3190
|
|
|
|
3191
|
4 |
|
if (($aCount > 0) && ($returnValue >= 0)) { |
3192
|
4 |
|
return sqrt($returnValue / $aCount); |
3193
|
|
|
} |
3194
|
|
|
} |
3195
|
|
|
|
3196
|
|
|
return Functions::DIV0(); |
3197
|
|
|
} |
3198
|
|
|
|
3199
|
|
|
/** |
3200
|
|
|
* STDEVPA. |
3201
|
|
|
* |
3202
|
|
|
* Calculates standard deviation based on the entire population, including numbers, text, and logical values |
3203
|
|
|
* |
3204
|
|
|
* Excel Function: |
3205
|
|
|
* STDEVPA(value1[,value2[, ...]]) |
3206
|
|
|
* |
3207
|
|
|
* @category Statistical Functions |
3208
|
|
|
* |
3209
|
|
|
* @param mixed ...$args Data values |
3210
|
|
|
* |
3211
|
|
|
* @return float|string |
3212
|
|
|
*/ |
3213
|
1 |
|
public static function STDEVPA(...$args) |
3214
|
|
|
{ |
3215
|
1 |
|
$aArgs = Functions::flattenArrayIndexed($args); |
3216
|
|
|
|
3217
|
1 |
|
$returnValue = null; |
3218
|
|
|
|
3219
|
1 |
|
$aMean = self::AVERAGEA($aArgs); |
3220
|
1 |
|
if ($aMean !== null) { |
|
|
|
|
3221
|
1 |
|
$aCount = 0; |
3222
|
1 |
|
foreach ($aArgs as $k => $arg) { |
3223
|
1 |
|
if ((is_bool($arg)) && |
3224
|
1 |
|
(!Functions::isMatrixValue($k))) { |
3225
|
|
|
} else { |
3226
|
|
|
// Is it a numeric value? |
3227
|
1 |
|
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) & ($arg != '')))) { |
|
|
|
|
3228
|
1 |
|
if (is_bool($arg)) { |
3229
|
1 |
|
$arg = (int) $arg; |
3230
|
1 |
|
} elseif (is_string($arg)) { |
3231
|
1 |
|
$arg = 0; |
3232
|
|
|
} |
3233
|
1 |
|
if ($returnValue === null) { |
3234
|
1 |
|
$returnValue = pow(($arg - $aMean), 2); |
3235
|
|
|
} else { |
3236
|
1 |
|
$returnValue += pow(($arg - $aMean), 2); |
3237
|
|
|
} |
3238
|
1 |
|
++$aCount; |
3239
|
|
|
} |
3240
|
|
|
} |
3241
|
|
|
} |
3242
|
|
|
|
3243
|
1 |
|
if (($aCount > 0) && ($returnValue >= 0)) { |
3244
|
1 |
|
return sqrt($returnValue / $aCount); |
3245
|
|
|
} |
3246
|
|
|
} |
3247
|
|
|
|
3248
|
|
|
return Functions::DIV0(); |
3249
|
|
|
} |
3250
|
|
|
|
3251
|
|
|
/** |
3252
|
|
|
* STEYX. |
3253
|
|
|
* |
3254
|
|
|
* Returns the standard error of the predicted y-value for each x in the regression. |
3255
|
|
|
* |
3256
|
|
|
* @param mixed[] $yValues Data Series Y |
3257
|
|
|
* @param mixed[] $xValues Data Series X |
3258
|
|
|
* |
3259
|
|
|
* @return float |
3260
|
|
|
*/ |
3261
|
|
|
public static function STEYX($yValues, $xValues) |
3262
|
|
|
{ |
3263
|
|
|
if (!self::checkTrendArrays($yValues, $xValues)) { |
3264
|
|
|
return Functions::VALUE(); |
|
|
|
|
3265
|
|
|
} |
3266
|
|
|
$yValueCount = count($yValues); |
3267
|
|
|
$xValueCount = count($xValues); |
3268
|
|
|
|
3269
|
|
|
if (($yValueCount == 0) || ($yValueCount != $xValueCount)) { |
3270
|
|
|
return Functions::NA(); |
|
|
|
|
3271
|
|
|
} elseif ($yValueCount == 1) { |
3272
|
|
|
return Functions::DIV0(); |
|
|
|
|
3273
|
|
|
} |
3274
|
|
|
|
3275
|
|
|
$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues); |
3276
|
|
|
|
3277
|
|
|
return $bestFitLinear->getStdevOfResiduals(); |
3278
|
|
|
} |
3279
|
|
|
|
3280
|
|
|
/** |
3281
|
|
|
* TDIST. |
3282
|
|
|
* |
3283
|
|
|
* Returns the probability of Student's T distribution. |
3284
|
|
|
* |
3285
|
|
|
* @param float $value Value for the function |
3286
|
|
|
* @param float $degrees degrees of freedom |
3287
|
|
|
* @param float $tails number of tails (1 or 2) |
3288
|
|
|
* |
3289
|
|
|
* @return float |
3290
|
|
|
*/ |
3291
|
|
|
public static function TDIST($value, $degrees, $tails) |
3292
|
|
|
{ |
3293
|
|
|
$value = Functions::flattenSingleValue($value); |
3294
|
|
|
$degrees = floor(Functions::flattenSingleValue($degrees)); |
3295
|
|
|
$tails = floor(Functions::flattenSingleValue($tails)); |
3296
|
|
|
|
3297
|
|
|
if ((is_numeric($value)) && (is_numeric($degrees)) && (is_numeric($tails))) { |
3298
|
|
|
if (($value < 0) || ($degrees < 1) || ($tails < 1) || ($tails > 2)) { |
3299
|
|
|
return Functions::NAN(); |
|
|
|
|
3300
|
|
|
} |
3301
|
|
|
// tdist, which finds the probability that corresponds to a given value |
3302
|
|
|
// of t with k degrees of freedom. This algorithm is translated from a |
3303
|
|
|
// pascal function on p81 of "Statistical Computing in Pascal" by D |
3304
|
|
|
// Cooke, A H Craven & G M Clark (1985: Edward Arnold (Pubs.) Ltd: |
3305
|
|
|
// London). The above Pascal algorithm is itself a translation of the |
3306
|
|
|
// fortran algoritm "AS 3" by B E Cooper of the Atlas Computer |
3307
|
|
|
// Laboratory as reported in (among other places) "Applied Statistics |
3308
|
|
|
// Algorithms", editied by P Griffiths and I D Hill (1985; Ellis |
3309
|
|
|
// Horwood Ltd.; W. Sussex, England). |
3310
|
|
|
$tterm = $degrees; |
3311
|
|
|
$ttheta = atan2($value, sqrt($tterm)); |
3312
|
|
|
$tc = cos($ttheta); |
3313
|
|
|
$ts = sin($ttheta); |
3314
|
|
|
$tsum = 0; |
|
|
|
|
3315
|
|
|
|
3316
|
|
|
if (($degrees % 2) == 1) { |
3317
|
|
|
$ti = 3; |
3318
|
|
|
$tterm = $tc; |
3319
|
|
|
} else { |
3320
|
|
|
$ti = 2; |
3321
|
|
|
$tterm = 1; |
3322
|
|
|
} |
3323
|
|
|
|
3324
|
|
|
$tsum = $tterm; |
3325
|
|
|
while ($ti < $degrees) { |
3326
|
|
|
$tterm *= $tc * $tc * ($ti - 1) / $ti; |
3327
|
|
|
$tsum += $tterm; |
3328
|
|
|
$ti += 2; |
3329
|
|
|
} |
3330
|
|
|
$tsum *= $ts; |
3331
|
|
|
if (($degrees % 2) == 1) { |
3332
|
|
|
$tsum = Functions::M_2DIVPI * ($tsum + $ttheta); |
3333
|
|
|
} |
3334
|
|
|
$tValue = 0.5 * (1 + $tsum); |
3335
|
|
|
if ($tails == 1) { |
3336
|
|
|
return 1 - abs($tValue); |
3337
|
|
|
} |
3338
|
|
|
|
3339
|
|
|
return 1 - abs((1 - $tValue) - $tValue); |
3340
|
|
|
} |
3341
|
|
|
|
3342
|
|
|
return Functions::VALUE(); |
|
|
|
|
3343
|
|
|
} |
3344
|
|
|
|
3345
|
|
|
/** |
3346
|
|
|
* TINV. |
3347
|
|
|
* |
3348
|
|
|
* Returns the one-tailed probability of the chi-squared distribution. |
3349
|
|
|
* |
3350
|
|
|
* @param float $probability Probability for the function |
3351
|
|
|
* @param float $degrees degrees of freedom |
3352
|
|
|
* |
3353
|
|
|
* @return float |
3354
|
|
|
*/ |
3355
|
|
|
public static function TINV($probability, $degrees) |
3356
|
|
|
{ |
3357
|
|
|
$probability = Functions::flattenSingleValue($probability); |
3358
|
|
|
$degrees = floor(Functions::flattenSingleValue($degrees)); |
3359
|
|
|
|
3360
|
|
|
if ((is_numeric($probability)) && (is_numeric($degrees))) { |
3361
|
|
|
$xLo = 100; |
3362
|
|
|
$xHi = 0; |
3363
|
|
|
|
3364
|
|
|
$x = $xNew = 1; |
3365
|
|
|
$dx = 1; |
3366
|
|
|
$i = 0; |
3367
|
|
|
|
3368
|
|
|
while ((abs($dx) > Functions::PRECISION) && ($i++ < self::MAX_ITERATIONS)) { |
3369
|
|
|
// Apply Newton-Raphson step |
3370
|
|
|
$result = self::TDIST($x, $degrees, 2); |
3371
|
|
|
$error = $result - $probability; |
3372
|
|
|
if ($error == 0.0) { |
3373
|
|
|
$dx = 0; |
3374
|
|
|
} elseif ($error < 0.0) { |
3375
|
|
|
$xLo = $x; |
3376
|
|
|
} else { |
3377
|
|
|
$xHi = $x; |
3378
|
|
|
} |
3379
|
|
|
// Avoid division by zero |
3380
|
|
|
if ($result != 0.0) { |
3381
|
|
|
$dx = $error / $result; |
3382
|
|
|
$xNew = $x - $dx; |
3383
|
|
|
} |
3384
|
|
|
// If the NR fails to converge (which for example may be the |
3385
|
|
|
// case if the initial guess is too rough) we apply a bisection |
3386
|
|
|
// step to determine a more narrow interval around the root. |
3387
|
|
|
if (($xNew < $xLo) || ($xNew > $xHi) || ($result == 0.0)) { |
3388
|
|
|
$xNew = ($xLo + $xHi) / 2; |
3389
|
|
|
$dx = $xNew - $x; |
3390
|
|
|
} |
3391
|
|
|
$x = $xNew; |
3392
|
|
|
} |
3393
|
|
|
if ($i == self::MAX_ITERATIONS) { |
3394
|
|
|
return Functions::NA(); |
|
|
|
|
3395
|
|
|
} |
3396
|
|
|
|
3397
|
|
|
return round($x, 12); |
3398
|
|
|
} |
3399
|
|
|
|
3400
|
|
|
return Functions::VALUE(); |
|
|
|
|
3401
|
|
|
} |
3402
|
|
|
|
3403
|
|
|
/** |
3404
|
|
|
* TREND. |
3405
|
|
|
* |
3406
|
|
|
* Returns values along a linear Trend |
3407
|
|
|
* |
3408
|
|
|
* @param mixed[] $yValues Data Series Y |
3409
|
|
|
* @param mixed[] $xValues Data Series X |
3410
|
|
|
* @param mixed[] $newValues Values of X for which we want to find Y |
3411
|
|
|
* @param bool $const a logical value specifying whether to force the intersect to equal 0 |
3412
|
|
|
* |
3413
|
|
|
* @return array of float |
3414
|
|
|
*/ |
3415
|
|
|
public static function TREND($yValues, $xValues = [], $newValues = [], $const = true) |
3416
|
|
|
{ |
3417
|
|
|
$yValues = Functions::flattenArray($yValues); |
3418
|
|
|
$xValues = Functions::flattenArray($xValues); |
3419
|
|
|
$newValues = Functions::flattenArray($newValues); |
3420
|
|
|
$const = ($const === null) ? true : (bool) Functions::flattenSingleValue($const); |
|
|
|
|
3421
|
|
|
|
3422
|
|
|
$bestFitLinear = Trend::calculate(Trend::TREND_LINEAR, $yValues, $xValues, $const); |
3423
|
|
|
if (empty($newValues)) { |
3424
|
|
|
$newValues = $bestFitLinear->getXValues(); |
3425
|
|
|
} |
3426
|
|
|
|
3427
|
|
|
$returnArray = []; |
3428
|
|
|
foreach ($newValues as $xValue) { |
3429
|
|
|
$returnArray[0][] = $bestFitLinear->getValueOfYForX($xValue); |
3430
|
|
|
} |
3431
|
|
|
|
3432
|
|
|
return $returnArray; |
3433
|
|
|
} |
3434
|
|
|
|
3435
|
|
|
/** |
3436
|
|
|
* TRIMMEAN. |
3437
|
|
|
* |
3438
|
|
|
* Returns the mean of the interior of a data set. TRIMMEAN calculates the mean |
3439
|
|
|
* taken by excluding a percentage of data points from the top and bottom tails |
3440
|
|
|
* of a data set. |
3441
|
|
|
* |
3442
|
|
|
* Excel Function: |
3443
|
|
|
* TRIMEAN(value1[,value2[, ...]], $discard) |
3444
|
|
|
* |
3445
|
|
|
* @category Statistical Functions |
3446
|
|
|
* |
3447
|
|
|
* @param mixed $args Data values |
3448
|
|
|
* @param float $discard Percentage to discard |
3449
|
|
|
* |
3450
|
|
|
* @return float|string |
3451
|
|
|
*/ |
3452
|
|
|
public static function TRIMMEAN(...$args) |
3453
|
|
|
{ |
3454
|
|
|
$aArgs = Functions::flattenArray($args); |
3455
|
|
|
|
3456
|
|
|
// Calculate |
3457
|
|
|
$percent = array_pop($aArgs); |
3458
|
|
|
|
3459
|
|
|
if ((is_numeric($percent)) && (!is_string($percent))) { |
3460
|
|
|
if (($percent < 0) || ($percent > 1)) { |
3461
|
|
|
return Functions::NAN(); |
3462
|
|
|
} |
3463
|
|
|
$mArgs = []; |
3464
|
|
|
foreach ($aArgs as $arg) { |
3465
|
|
|
// Is it a numeric value? |
3466
|
|
|
if ((is_numeric($arg)) && (!is_string($arg))) { |
3467
|
|
|
$mArgs[] = $arg; |
3468
|
|
|
} |
3469
|
|
|
} |
3470
|
|
|
$discard = floor(self::COUNT($mArgs) * $percent / 2); |
3471
|
|
|
sort($mArgs); |
3472
|
|
|
for ($i = 0; $i < $discard; ++$i) { |
3473
|
|
|
array_pop($mArgs); |
3474
|
|
|
array_shift($mArgs); |
3475
|
|
|
} |
3476
|
|
|
|
3477
|
|
|
return self::AVERAGE($mArgs); |
3478
|
|
|
} |
3479
|
|
|
|
3480
|
|
|
return Functions::VALUE(); |
3481
|
|
|
} |
3482
|
|
|
|
3483
|
|
|
/** |
3484
|
|
|
* VARFunc. |
3485
|
|
|
* |
3486
|
|
|
* Estimates variance based on a sample. |
3487
|
|
|
* |
3488
|
|
|
* Excel Function: |
3489
|
|
|
* VAR(value1[,value2[, ...]]) |
3490
|
|
|
* |
3491
|
|
|
* @category Statistical Functions |
3492
|
|
|
* |
3493
|
|
|
* @param mixed ...$args Data values |
3494
|
|
|
* |
3495
|
|
|
* @return float |
3496
|
|
|
*/ |
3497
|
4 |
|
public static function VARFunc(...$args) |
3498
|
|
|
{ |
3499
|
4 |
|
$returnValue = Functions::DIV0(); |
3500
|
|
|
|
3501
|
4 |
|
$summerA = $summerB = 0; |
3502
|
|
|
|
3503
|
|
|
// Loop through arguments |
3504
|
4 |
|
$aArgs = Functions::flattenArray($args); |
3505
|
4 |
|
$aCount = 0; |
3506
|
4 |
|
foreach ($aArgs as $arg) { |
3507
|
4 |
|
if (is_bool($arg)) { |
3508
|
1 |
|
$arg = (int) $arg; |
3509
|
|
|
} |
3510
|
|
|
// Is it a numeric value? |
3511
|
4 |
|
if ((is_numeric($arg)) && (!is_string($arg))) { |
3512
|
4 |
|
$summerA += ($arg * $arg); |
3513
|
4 |
|
$summerB += $arg; |
3514
|
4 |
|
++$aCount; |
3515
|
|
|
} |
3516
|
|
|
} |
3517
|
|
|
|
3518
|
4 |
|
if ($aCount > 1) { |
3519
|
4 |
|
$summerA *= $aCount; |
3520
|
4 |
|
$summerB *= $summerB; |
3521
|
4 |
|
$returnValue = ($summerA - $summerB) / ($aCount * ($aCount - 1)); |
3522
|
|
|
} |
3523
|
|
|
|
3524
|
4 |
|
return $returnValue; |
|
|
|
|
3525
|
|
|
} |
3526
|
|
|
|
3527
|
|
|
/** |
3528
|
|
|
* VARA. |
3529
|
|
|
* |
3530
|
|
|
* Estimates variance based on a sample, including numbers, text, and logical values |
3531
|
|
|
* |
3532
|
|
|
* Excel Function: |
3533
|
|
|
* VARA(value1[,value2[, ...]]) |
3534
|
|
|
* |
3535
|
|
|
* @category Statistical Functions |
3536
|
|
|
* |
3537
|
|
|
* @param mixed ...$args Data values |
3538
|
|
|
* |
3539
|
|
|
* @return float |
3540
|
|
|
*/ |
3541
|
1 |
|
public static function VARA(...$args) |
3542
|
|
|
{ |
3543
|
1 |
|
$returnValue = Functions::DIV0(); |
3544
|
|
|
|
3545
|
1 |
|
$summerA = $summerB = 0; |
3546
|
|
|
|
3547
|
|
|
// Loop through arguments |
3548
|
1 |
|
$aArgs = Functions::flattenArrayIndexed($args); |
3549
|
1 |
|
$aCount = 0; |
3550
|
1 |
|
foreach ($aArgs as $k => $arg) { |
3551
|
1 |
|
if ((is_string($arg)) && |
3552
|
1 |
|
(Functions::isValue($k))) { |
3553
|
|
|
return Functions::VALUE(); |
|
|
|
|
3554
|
1 |
|
} elseif ((is_string($arg)) && |
3555
|
1 |
|
(!Functions::isMatrixValue($k))) { |
3556
|
|
|
} else { |
3557
|
|
|
// Is it a numeric value? |
3558
|
1 |
|
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) & ($arg != '')))) { |
|
|
|
|
3559
|
1 |
|
if (is_bool($arg)) { |
3560
|
1 |
|
$arg = (int) $arg; |
3561
|
1 |
|
} elseif (is_string($arg)) { |
3562
|
1 |
|
$arg = 0; |
3563
|
|
|
} |
3564
|
1 |
|
$summerA += ($arg * $arg); |
3565
|
1 |
|
$summerB += $arg; |
3566
|
1 |
|
++$aCount; |
3567
|
|
|
} |
3568
|
|
|
} |
3569
|
|
|
} |
3570
|
|
|
|
3571
|
1 |
|
if ($aCount > 1) { |
3572
|
1 |
|
$summerA *= $aCount; |
3573
|
1 |
|
$summerB *= $summerB; |
3574
|
1 |
|
$returnValue = ($summerA - $summerB) / ($aCount * ($aCount - 1)); |
3575
|
|
|
} |
3576
|
|
|
|
3577
|
1 |
|
return $returnValue; |
|
|
|
|
3578
|
|
|
} |
3579
|
|
|
|
3580
|
|
|
/** |
3581
|
|
|
* VARP. |
3582
|
|
|
* |
3583
|
|
|
* Calculates variance based on the entire population |
3584
|
|
|
* |
3585
|
|
|
* Excel Function: |
3586
|
|
|
* VARP(value1[,value2[, ...]]) |
3587
|
|
|
* |
3588
|
|
|
* @category Statistical Functions |
3589
|
|
|
* |
3590
|
|
|
* @param mixed ...$args Data values |
3591
|
|
|
* |
3592
|
|
|
* @return float |
3593
|
|
|
*/ |
3594
|
4 |
|
public static function VARP(...$args) |
3595
|
|
|
{ |
3596
|
|
|
// Return value |
3597
|
4 |
|
$returnValue = Functions::DIV0(); |
3598
|
|
|
|
3599
|
4 |
|
$summerA = $summerB = 0; |
3600
|
|
|
|
3601
|
|
|
// Loop through arguments |
3602
|
4 |
|
$aArgs = Functions::flattenArray($args); |
3603
|
4 |
|
$aCount = 0; |
3604
|
4 |
|
foreach ($aArgs as $arg) { |
3605
|
4 |
|
if (is_bool($arg)) { |
3606
|
1 |
|
$arg = (int) $arg; |
3607
|
|
|
} |
3608
|
|
|
// Is it a numeric value? |
3609
|
4 |
|
if ((is_numeric($arg)) && (!is_string($arg))) { |
3610
|
4 |
|
$summerA += ($arg * $arg); |
3611
|
4 |
|
$summerB += $arg; |
3612
|
4 |
|
++$aCount; |
3613
|
|
|
} |
3614
|
|
|
} |
3615
|
|
|
|
3616
|
4 |
|
if ($aCount > 0) { |
3617
|
4 |
|
$summerA *= $aCount; |
3618
|
4 |
|
$summerB *= $summerB; |
3619
|
4 |
|
$returnValue = ($summerA - $summerB) / ($aCount * $aCount); |
3620
|
|
|
} |
3621
|
|
|
|
3622
|
4 |
|
return $returnValue; |
|
|
|
|
3623
|
|
|
} |
3624
|
|
|
|
3625
|
|
|
/** |
3626
|
|
|
* VARPA. |
3627
|
|
|
* |
3628
|
|
|
* Calculates variance based on the entire population, including numbers, text, and logical values |
3629
|
|
|
* |
3630
|
|
|
* Excel Function: |
3631
|
|
|
* VARPA(value1[,value2[, ...]]) |
3632
|
|
|
* |
3633
|
|
|
* @category Statistical Functions |
3634
|
|
|
* |
3635
|
|
|
* @param mixed ...$args Data values |
3636
|
|
|
* |
3637
|
|
|
* @return float |
3638
|
|
|
*/ |
3639
|
1 |
|
public static function VARPA(...$args) |
3640
|
|
|
{ |
3641
|
1 |
|
$returnValue = Functions::DIV0(); |
3642
|
|
|
|
3643
|
1 |
|
$summerA = $summerB = 0; |
3644
|
|
|
|
3645
|
|
|
// Loop through arguments |
3646
|
1 |
|
$aArgs = Functions::flattenArrayIndexed($args); |
3647
|
1 |
|
$aCount = 0; |
3648
|
1 |
|
foreach ($aArgs as $k => $arg) { |
3649
|
1 |
|
if ((is_string($arg)) && |
3650
|
1 |
|
(Functions::isValue($k))) { |
3651
|
|
|
return Functions::VALUE(); |
|
|
|
|
3652
|
1 |
|
} elseif ((is_string($arg)) && |
3653
|
1 |
|
(!Functions::isMatrixValue($k))) { |
3654
|
|
|
} else { |
3655
|
|
|
// Is it a numeric value? |
3656
|
1 |
|
if ((is_numeric($arg)) || (is_bool($arg)) || ((is_string($arg) & ($arg != '')))) { |
|
|
|
|
3657
|
1 |
|
if (is_bool($arg)) { |
3658
|
1 |
|
$arg = (int) $arg; |
3659
|
1 |
|
} elseif (is_string($arg)) { |
3660
|
1 |
|
$arg = 0; |
3661
|
|
|
} |
3662
|
1 |
|
$summerA += ($arg * $arg); |
3663
|
1 |
|
$summerB += $arg; |
3664
|
1 |
|
++$aCount; |
3665
|
|
|
} |
3666
|
|
|
} |
3667
|
|
|
} |
3668
|
|
|
|
3669
|
1 |
|
if ($aCount > 0) { |
3670
|
1 |
|
$summerA *= $aCount; |
3671
|
1 |
|
$summerB *= $summerB; |
3672
|
1 |
|
$returnValue = ($summerA - $summerB) / ($aCount * $aCount); |
3673
|
|
|
} |
3674
|
|
|
|
3675
|
1 |
|
return $returnValue; |
|
|
|
|
3676
|
|
|
} |
3677
|
|
|
|
3678
|
|
|
/** |
3679
|
|
|
* WEIBULL. |
3680
|
|
|
* |
3681
|
|
|
* Returns the Weibull distribution. Use this distribution in reliability |
3682
|
|
|
* analysis, such as calculating a device's mean time to failure. |
3683
|
|
|
* |
3684
|
|
|
* @param float $value |
3685
|
|
|
* @param float $alpha Alpha Parameter |
3686
|
|
|
* @param float $beta Beta Parameter |
3687
|
|
|
* @param bool $cumulative |
3688
|
|
|
* |
3689
|
|
|
* @return float |
3690
|
|
|
*/ |
3691
|
|
|
public static function WEIBULL($value, $alpha, $beta, $cumulative) |
3692
|
|
|
{ |
3693
|
|
|
$value = Functions::flattenSingleValue($value); |
3694
|
|
|
$alpha = Functions::flattenSingleValue($alpha); |
3695
|
|
|
$beta = Functions::flattenSingleValue($beta); |
3696
|
|
|
|
3697
|
|
|
if ((is_numeric($value)) && (is_numeric($alpha)) && (is_numeric($beta))) { |
3698
|
|
|
if (($value < 0) || ($alpha <= 0) || ($beta <= 0)) { |
3699
|
|
|
return Functions::NAN(); |
|
|
|
|
3700
|
|
|
} |
3701
|
|
|
if ((is_numeric($cumulative)) || (is_bool($cumulative))) { |
|
|
|
|
3702
|
|
|
if ($cumulative) { |
3703
|
|
|
return 1 - exp(0 - pow($value / $beta, $alpha)); |
3704
|
|
|
} |
3705
|
|
|
|
3706
|
|
|
return ($alpha / pow($beta, $alpha)) * pow($value, $alpha - 1) * exp(0 - pow($value / $beta, $alpha)); |
3707
|
|
|
} |
3708
|
|
|
} |
3709
|
|
|
|
3710
|
|
|
return Functions::VALUE(); |
|
|
|
|
3711
|
|
|
} |
3712
|
|
|
|
3713
|
|
|
/** |
3714
|
|
|
* ZTEST. |
3715
|
|
|
* |
3716
|
|
|
* Returns the Weibull distribution. Use this distribution in reliability |
3717
|
|
|
* analysis, such as calculating a device's mean time to failure. |
3718
|
|
|
* |
3719
|
|
|
* @param float $dataSet |
3720
|
|
|
* @param float $m0 Alpha Parameter |
3721
|
|
|
* @param float $sigma Beta Parameter |
3722
|
|
|
* |
3723
|
|
|
* @return float|string |
3724
|
|
|
*/ |
3725
|
|
|
public static function ZTEST($dataSet, $m0, $sigma = null) |
3726
|
|
|
{ |
3727
|
|
|
$dataSet = Functions::flattenArrayIndexed($dataSet); |
|
|
|
|
3728
|
|
|
$m0 = Functions::flattenSingleValue($m0); |
3729
|
|
|
$sigma = Functions::flattenSingleValue($sigma); |
3730
|
|
|
|
3731
|
|
|
if ($sigma === null) { |
3732
|
|
|
$sigma = self::STDEV($dataSet); |
3733
|
|
|
} |
3734
|
|
|
$n = count($dataSet); |
3735
|
|
|
|
3736
|
|
|
return 1 - self::NORMSDIST((self::AVERAGE($dataSet) - $m0) / ($sigma / sqrt($n))); |
3737
|
|
|
} |
3738
|
|
|
} |
3739
|
|
|
|