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<?php |
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namespace Samsara\Fermat\Stats\Values\Distribution; |
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use ReflectionException; |
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use Samsara\Exceptions\UsageError\IntegrityConstraint; |
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use Samsara\Exceptions\UsageError\OptionalExit; |
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use Samsara\Fermat\Core\Numbers; |
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use Samsara\Fermat\Stats\Types\Distribution; |
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use Samsara\Fermat\Core\Provider\RandomProvider; |
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use Samsara\Fermat\Core\Provider\SequenceProvider; |
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use Samsara\Fermat\Stats\Provider\StatsProvider; |
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use Samsara\Fermat\Core\Types\Base\Interfaces\Numbers\DecimalInterface; |
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use Samsara\Fermat\Expressions\Types\Base\Interfaces\Evaluateables\FunctionInterface; |
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use Samsara\Fermat\Core\Types\Base\Interfaces\Numbers\NumberInterface; |
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use Samsara\Fermat\Core\Types\NumberCollection; |
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use Samsara\Fermat\Core\Values\ImmutableDecimal; |
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class Normal extends Distribution |
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{ |
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/** |
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* @var ImmutableDecimal |
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*/ |
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private $mean; |
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/** |
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* @var ImmutableDecimal |
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*/ |
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private $sd; |
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/** |
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* Normal constructor. |
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* |
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* @param int|float|DecimalInterface $mean |
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* @param int|float|DecimalInterface $sd |
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* |
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* @throws IntegrityConstraint |
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* @throws ReflectionException |
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*/ |
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public function __construct($mean, $sd) |
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{ |
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/** @var ImmutableDecimal $mean */ |
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$mean = Numbers::makeOrDont(Numbers::IMMUTABLE, $mean); |
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/** @var ImmutableDecimal $sd */ |
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$sd = Numbers::makeOrDont(Numbers::IMMUTABLE, $sd); |
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$this->mean = $mean; |
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$this->sd = $sd; |
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} |
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/** |
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* @return ImmutableDecimal |
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*/ |
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public function getSD(): ImmutableDecimal |
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{ |
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return $this->sd; |
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} |
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/** |
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* @return ImmutableDecimal |
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*/ |
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public function getMean(): ImmutableDecimal |
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{ |
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return $this->mean; |
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} |
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/** |
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* @param $x |
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* |
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* @return ImmutableDecimal |
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* @throws IntegrityConstraint |
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* @throws ReflectionException |
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*/ |
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public function evaluateAt($x, int $scale = 10): ImmutableDecimal |
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{ |
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$one = Numbers::makeOne($scale); |
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$twoPi = Numbers::make2Pi($scale); |
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$e = Numbers::makeE($scale); |
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$x = Numbers::makeOrDont(Numbers::IMMUTABLE, $x); |
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$internalScale = (new NumberCollection([$scale, $x]))->selectScale() + 2; |
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// $left = 1 / ( sqrt(2pi * SD^2) ) |
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$left = |
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$one->divide( |
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$twoPi->multiply( |
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$this->getSD() |
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->pow(2) |
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)->sqrt($internalScale), |
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$internalScale |
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); |
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// $right = e^( -1*((x - SD)^2)/(2*SD^2) ) |
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$right = |
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$e->pow( |
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$x->subtract( |
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$this->getMean() |
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)->pow(2) |
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->divide( |
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$this->getSD() |
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->pow(2) |
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->multiply(2), |
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$internalScale |
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)->multiply(-1) |
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); |
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// Return value is not inlined to ensure proper return type for IDE |
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/** @var ImmutableDecimal $value */ |
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$value = $left->multiply($right)->truncateToScale($scale); |
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return $value; |
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} |
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/** |
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* @param int|float|DecimalInterface $p |
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* @param int|float|DecimalInterface $x |
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* @param int|float|DecimalInterface $mean |
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* |
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* @return Normal |
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* @throws IntegrityConstraint |
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* @throws OptionalExit |
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* @throws ReflectionException |
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*/ |
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public static function makeFromMean($p, $x, $mean): Normal |
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{ |
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$one = Numbers::makeOne(10); |
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$p = Numbers::makeOrDont(Numbers::IMMUTABLE, $p); |
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$x = Numbers::makeOrDont(Numbers::IMMUTABLE, $x); |
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$mean = Numbers::makeOrDont(Numbers::IMMUTABLE, $mean); |
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$internalScale = (new NumberCollection([$one, $p, $x, $mean]))->selectScale(); |
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$internalScale += 2; |
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$z = StatsProvider::inverseNormalCDF($one->subtract($p), $internalScale); |
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$sd = |
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$x->subtract($mean) |
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->divide( |
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$z, |
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$internalScale |
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)->abs() |
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->truncateToScale($internalScale-2); |
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return new Normal($mean, $sd); |
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} |
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/** |
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* @param int|float|DecimalInterface $p |
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* @param int|float|DecimalInterface $x |
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* @param int|float|DecimalInterface $sd |
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* |
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* @return Normal |
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* @throws IntegrityConstraint |
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* @throws OptionalExit |
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* @throws ReflectionException |
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*/ |
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public static function makeFromSd($p, $x, $sd): Normal |
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{ |
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$one = Numbers::makeOne(10); |
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$p = Numbers::makeOrDont(Numbers::IMMUTABLE, $p); |
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$x = Numbers::makeOrDont(Numbers::IMMUTABLE, $x); |
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$sd = Numbers::makeOrDont(Numbers::IMMUTABLE, $sd); |
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$internalScale = (new NumberCollection([$one, $p, $x, $sd]))->selectScale(); |
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$internalScale += 2; |
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$z = StatsProvider::inverseNormalCDF($one->subtract($p), $internalScale); |
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$mean = |
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$x->add( |
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$z->multiply($sd) |
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)->truncateToScale($internalScale-2); |
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return new Normal($mean, $sd); |
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} |
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/** |
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* @param int|float|DecimalInterface $x |
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* |
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* @return ImmutableDecimal |
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* @throws IntegrityConstraint |
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* @throws OptionalExit |
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* @throws ReflectionException |
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*/ |
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public function cdf($x): ImmutableDecimal |
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{ |
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$x = Numbers::makeOrDont(Numbers::IMMUTABLE, $x); |
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$oneHalf = Numbers::make(Numbers::IMMUTABLE, '0.5'); |
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$one = Numbers::makeOne(); |
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$sqrtTwo = Numbers::make(Numbers::IMMUTABLE, 2)->sqrt(); |
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/** @var ImmutableDecimal $cdf */ |
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$cdf = |
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$oneHalf->multiply( |
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$one->add( |
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StatsProvider::gaussErrorFunction( |
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$x->subtract($this->mean) |
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->divide( |
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$this->sd->multiply($sqrtTwo) |
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) |
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) |
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) |
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); |
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return $cdf; |
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} |
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/** |
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* @param int|float|DecimalInterface $x1 |
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* @param null|int|float|DecimalInterface $x2 |
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* |
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* @return ImmutableDecimal |
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* @throws IntegrityConstraint |
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* @throws ReflectionException |
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*/ |
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public function pdf($x1, $x2 = null): ImmutableDecimal |
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{ |
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$x1 = Numbers::makeOrDont(Numbers::IMMUTABLE, $x1); |
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if (is_null($x2)) { |
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$separation = $x1->subtract($this->mean)->multiply(2)->abs(); |
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if ($this->mean->isLessThan($x1)) { |
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$x2 = $x1->subtract($separation); |
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} else { |
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$x2 = $x1->add($separation); |
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} |
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} |
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/** @var ImmutableDecimal $pdf */ |
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$pdf = |
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$this->cdf($x1) |
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->subtract( |
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$this->cdf($x2) |
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)->abs(); |
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return $pdf; |
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} |
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/** |
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* @param FunctionInterface $function |
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* @param $x |
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* @return ImmutableDecimal |
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* @throws IntegrityConstraint |
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* @throws ReflectionException |
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*/ |
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public function cdfProduct(FunctionInterface $function, $x): ImmutableDecimal |
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{ |
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$loop = 0; |
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$cdf = Numbers::makeZero(); |
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while (true) { |
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if (count($function->describeShape()) === 0) { |
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break; |
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} |
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$cdf = $cdf->add($function->evaluateAt($x)->multiply(SequenceProvider::nthPowerNegativeOne($loop))); |
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$function = $function->derivativeExpression(); |
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} |
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/** @var ImmutableDecimal $cdf */ |
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$cdf = $cdf->multiply($this->cdf($x)); |
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return $cdf; |
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} |
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/** |
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* @param FunctionInterface $function |
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* @param $x1 |
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* @param $x2 |
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* |
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* @return ImmutableDecimal |
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* @throws IntegrityConstraint |
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* @throws ReflectionException |
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*/ |
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public function pdfProduct(FunctionInterface $function, $x1, $x2): ImmutableDecimal |
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{ |
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/** @var ImmutableDecimal $pdf */ |
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$pdf = $this->cdfProduct($function, $x2)->subtract($this->cdfProduct($function, $x1)); |
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return $pdf; |
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} |
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/** |
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* @param int|float|DecimalInterface $x |
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* |
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* @return ImmutableDecimal |
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* @throws IntegrityConstraint |
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*/ |
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public function percentBelowX($x): ImmutableDecimal |
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{ |
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return $this->cdf($x); |
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} |
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/** |
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* @param int|float|DecimalInterface $x |
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* |
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* @return ImmutableDecimal |
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* @throws IntegrityConstraint |
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* @throws ReflectionException |
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*/ |
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2 |
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public function percentAboveX($x): ImmutableDecimal |
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{ |
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2 |
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$one = Numbers::makeOne(); |
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/** @var ImmutableDecimal $perc */ |
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2 |
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$perc = $one->subtract($this->cdf($x)); |
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2 |
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return $perc; |
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} |
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/** |
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* @param int|float|DecimalInterface $x |
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* |
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* @return ImmutableDecimal |
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* @throws IntegrityConstraint |
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* @throws ReflectionException |
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*/ |
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329
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public function zScoreOfX($x): ImmutableDecimal |
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330
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{ |
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/** @var ImmutableDecimal $x */ |
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332
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$x = Numbers::makeOrDont(Numbers::IMMUTABLE, $x); |
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333
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334
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/** @var ImmutableDecimal $z */ |
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335
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$z = $x->subtract($this->mean)->divide($this->sd); |
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336
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|
|
|
return $z; |
|
338
|
|
|
} |
|
339
|
|
|
|
|
340
|
|
|
/** |
|
341
|
|
|
* @param int|float|DecimalInterface $z |
|
342
|
|
|
* |
|
343
|
|
|
* @return ImmutableDecimal |
|
344
|
|
|
* @throws IntegrityConstraint |
|
345
|
|
|
* @throws ReflectionException |
|
346
|
|
|
*/ |
|
347
|
|
|
public function xFromZScore($z): ImmutableDecimal |
|
348
|
|
|
{ |
|
349
|
|
|
$z = Numbers::makeOrDont(Numbers::IMMUTABLE, $z); |
|
350
|
|
|
|
|
351
|
|
|
/** @var ImmutableDecimal $x */ |
|
352
|
|
|
$x = $z->multiply($this->sd)->add($this->mean); |
|
353
|
|
|
|
|
354
|
|
|
return $x; |
|
355
|
|
|
} |
|
356
|
|
|
|
|
357
|
|
|
/** |
|
358
|
|
|
* @return ImmutableDecimal |
|
359
|
|
|
* @throws IntegrityConstraint |
|
360
|
|
|
* @throws ReflectionException |
|
361
|
|
|
* |
|
362
|
|
|
* @codeCoverageIgnore |
|
363
|
|
|
*/ |
|
364
|
|
|
public function random(): ImmutableDecimal |
|
365
|
|
|
{ |
|
366
|
|
|
$rand1 = RandomProvider::randomDecimal(20); |
|
367
|
|
|
$rand2 = RandomProvider::randomDecimal(20); |
|
368
|
|
|
|
|
369
|
|
|
$randomNumber = |
|
370
|
|
|
$rand1->ln() |
|
371
|
|
|
->multiply(-2) |
|
372
|
|
|
->sqrt() |
|
373
|
|
|
->multiply( |
|
374
|
|
|
$rand2->multiply(Numbers::TAU) |
|
375
|
|
|
->cos(1, false) |
|
376
|
|
|
); |
|
377
|
|
|
/** @var ImmutableDecimal $randomNumber */ |
|
378
|
|
|
$randomNumber = $randomNumber->multiply($this->sd)->add($this->mean); |
|
379
|
|
|
|
|
380
|
|
|
return $randomNumber; |
|
381
|
|
|
} |
|
382
|
|
|
|
|
383
|
|
|
/** |
|
384
|
|
|
* @param int|float|NumberInterface $min |
|
385
|
|
|
* @param int|float|NumberInterface $max |
|
386
|
|
|
* @param int $maxIterations |
|
387
|
|
|
* |
|
388
|
|
|
* @return ImmutableDecimal |
|
389
|
|
|
* @throws OptionalExit |
|
390
|
|
|
* @throws IntegrityConstraint |
|
391
|
|
|
* @throws ReflectionException |
|
392
|
|
|
* |
|
393
|
|
|
* @codeCoverageIgnore |
|
394
|
|
|
*/ |
|
395
|
|
|
public function rangeRandom($min = 0, $max = PHP_INT_MAX, int $maxIterations = 20): ImmutableDecimal |
|
396
|
|
|
{ |
|
397
|
|
|
$i = 0; |
|
398
|
|
|
|
|
399
|
|
|
do { |
|
400
|
|
|
$randomNumber = $this->random(); |
|
401
|
|
|
$i++; |
|
402
|
|
|
} while (($randomNumber->isGreaterThan($max) || $randomNumber->isLessThan($min)) && $i < $maxIterations); |
|
403
|
|
|
|
|
404
|
|
|
if ($randomNumber->isGreaterThan($max) || $randomNumber->isLessThan($min)) { |
|
405
|
|
|
throw new OptionalExit( |
|
406
|
|
|
'All random numbers generated were outside of the requested range', |
|
407
|
|
|
'Widen the acceptable range of random values, or allow the function to perform mor iterations', |
|
408
|
|
|
'A suitable random number, restricted by the $max ('.$max.') and $min ('.$min.'), could not be found within '.$maxIterations.' iterations' |
|
|
|
|
|
|
409
|
|
|
); |
|
410
|
|
|
} |
|
411
|
|
|
|
|
412
|
|
|
return $randomNumber; |
|
413
|
|
|
} |
|
414
|
|
|
|
|
415
|
|
|
} |
JordanRL /
Fermat
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