HuasoFoundries /
math_histogram
| Total Complexity | 231 |
| Total Lines | 1698 |
| Duplicated Lines | 0 % |
| Changes | 0 | ||
Complex classes like Stats often do a lot of different things. To break such a class down, we need to identify a cohesive component within that class. A common approach to find such a component is to look for fields/methods that share the same prefixes, or suffixes.
Once you have determined the fields that belong together, you can apply the Extract Class refactoring. If the component makes sense as a sub-class, Extract Subclass is also a candidate, and is often faster.
While breaking up the class, it is a good idea to analyze how other classes use Stats, and based on these observations, apply Extract Interface, too.
| 1 | <?php |
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| 12 | class Stats |
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| 13 | { |
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| 14 | |||
| 15 | // Constants for defining the statistics to calculate |
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| 16 | /** |
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| 17 | * STATS_BASIC to generate the basic descriptive statistics |
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| 18 | */ |
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| 19 | const STATS_BASIC = 1; |
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| 20 | /** |
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| 21 | * STATS_FULL to generate also higher moments, mode, median, etc. |
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| 22 | */ |
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| 23 | const STATS_FULL = 2; |
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| 24 | |||
| 25 | // Constants describing the data set format |
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| 26 | /** |
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| 27 | * STATS_DATA_SIMPLE for an array of numeric values. This is the default. |
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| 28 | * e.g. $data = array(2,3,4,5,1,1,6); |
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| 29 | */ |
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| 30 | const STATS_DATA_SIMPLE = 0; |
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| 31 | /** |
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| 32 | * STATS_DATA_CUMMULATIVE for an associative array of frequency values, |
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| 33 | * where in each array entry, the index is the data point and the |
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| 34 | * value the count (frequency): |
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| 35 | * e.g. $data = array(3=>4, 2.3=>5, 1.25=>6, 0.5=>3) |
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| 36 | */ |
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| 37 | const STATS_DATA_CUMMULATIVE = 1; |
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| 38 | |||
| 39 | // Constants defining how to handle nulls |
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| 40 | /** |
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| 41 | * STATS_REJECT_NULL, reject data sets with null values. This is the default. |
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| 42 | * Any non-numeric value is considered a null in this context. |
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| 43 | */ |
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| 44 | const STATS_REJECT_NULL = -1; |
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| 45 | /** |
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| 46 | * STATS_IGNORE_NULL, ignore null values and prune them from the data. |
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| 47 | * Any non-numeric value is considered a null in this context. |
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| 48 | */ |
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| 49 | const STATS_IGNORE_NULL = -2; |
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| 50 | /** |
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| 51 | * STATS_USE_NULL_AS_ZERO, assign the value of 0 (zero) to null values. |
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| 52 | * Any non-numeric value is considered a null in this context. |
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| 53 | */ |
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| 54 | const STATS_USE_NULL_AS_ZERO = -3; |
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| 55 | |||
| 56 | // properties |
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| 57 | |||
| 58 | /** |
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| 59 | * The simple or cummulative data set. |
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| 60 | * Null by default. |
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| 61 | * |
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| 62 | * @access private |
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| 63 | * @var array |
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| 64 | */ |
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| 65 | private $_data = null; |
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| 66 | |||
| 67 | /** |
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| 68 | * Expanded data set. Only set when cummulative data |
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| 69 | * is being used. Null by default. |
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| 70 | * |
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| 71 | * @access private |
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| 72 | * @var array |
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| 73 | */ |
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| 74 | private $_dataExpanded = null; |
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| 75 | |||
| 76 | /** |
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| 77 | * Flag for data type, one of STATS_DATA_SIMPLE or |
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| 78 | * STATS_DATA_CUMMULATIVE. Null by default. |
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| 79 | * |
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| 80 | * @access private |
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| 81 | * @var int |
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| 82 | */ |
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| 83 | private $_dataOption = null; |
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| 84 | |||
| 85 | /** |
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| 86 | * Flag for null handling options. One of STATS_REJECT_NULL, |
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| 87 | * STATS_IGNORE_NULL or STATS_USE_NULL_AS_ZERO |
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| 88 | * |
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| 89 | * @access private |
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| 90 | * @var int |
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| 91 | */ |
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| 92 | private $_nullOption; |
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| 93 | |||
| 94 | /** |
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| 95 | * Array for caching result values, should be reset |
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| 96 | * when using setData() |
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| 97 | * |
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| 98 | * @access private |
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| 99 | * @var array |
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| 100 | */ |
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| 101 | private $_calculatedValues = array(); |
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| 102 | |||
| 103 | /** |
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| 104 | * Constructor for the class |
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| 105 | * |
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| 106 | * @access public |
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| 107 | * @param optional int $nullOption how to handle null values |
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| 108 | * @return object Math_Stats |
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| 109 | */ |
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| 110 | public function __construct($nullOption = self::STATS_REJECT_NULL) |
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| 111 | { |
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| 112 | $this->_nullOption = $nullOption; |
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| 113 | } |
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| 114 | |||
| 115 | /** |
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| 116 | * Sets and verifies the data, checking for nulls and using |
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| 117 | * the current null handling option |
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| 118 | * |
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| 119 | * @access public |
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| 120 | * @param array $arr the data set |
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| 121 | * @param optional int $opt data format: STATS_DATA_CUMMULATIVE or STATS_DATA_SIMPLE (default) |
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| 122 | * @return mixed true on success, a PEAR_Error object otherwise |
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| 123 | */ |
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| 124 | public function setData($arr, $opt = self::STATS_DATA_SIMPLE) |
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| 125 | { |
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| 126 | if (!is_array($arr)) { |
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|
introduced
by
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| 127 | throw new \PEAR_Exception('invalid data, an array of numeric data was expected'); |
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| 128 | } |
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| 129 | $this->_data = null; |
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| 130 | $this->_dataExpanded = null; |
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| 131 | $this->_dataOption = null; |
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| 132 | $this->_calculatedValues = array(); |
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| 133 | if ($opt == self::STATS_DATA_SIMPLE) { |
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| 134 | $this->_dataOption = $opt; |
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| 135 | $this->_data = array_values($arr); |
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| 136 | } elseif ($opt == self::STATS_DATA_CUMMULATIVE) { |
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| 137 | $this->_dataOption = $opt; |
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| 138 | $this->_data = $arr; |
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| 139 | $this->_dataExpanded = array(); |
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| 140 | } |
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| 141 | return $this->_validate(); |
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| 142 | } |
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| 143 | |||
| 144 | /** |
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| 145 | * Returns the data which might have been modified |
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| 146 | * according to the current null handling options. |
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| 147 | * |
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| 148 | * @access public |
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| 149 | * @param boolean $expanded whether to return a expanded list, default is false |
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| 150 | * @return mixed array of data on success, a PEAR_Error object otherwise |
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| 151 | * @see _validate() |
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| 152 | */ |
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| 153 | public function getData($expanded = false) |
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| 154 | { |
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| 155 | if ($this->_data == null) { |
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| 156 | throw new \PEAR_Exception('data has not been set'); |
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| 157 | } |
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| 158 | if ($this->_dataOption == self::STATS_DATA_CUMMULATIVE && $expanded) { |
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| 159 | return $this->_dataExpanded; |
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| 160 | } else { |
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| 161 | return $this->_data; |
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| 162 | } |
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| 163 | } |
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| 164 | |||
| 165 | /** |
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| 166 | * Sets the null handling option. |
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| 167 | * Must be called before assigning a new data set containing null values |
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| 168 | * |
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| 169 | * @access public |
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| 170 | * @return mixed true on success, a PEAR_Error object otherwise |
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| 171 | * @see _validate() |
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| 172 | */ |
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| 173 | public function setNullOption($nullOption) |
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| 174 | { |
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| 175 | if ($nullOption == self::STATS_REJECT_NULL |
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| 176 | || $nullOption == self::STATS_IGNORE_NULL |
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| 177 | || $nullOption == self::STATS_USE_NULL_AS_ZERO) { |
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| 178 | $this->_nullOption = $nullOption; |
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| 179 | return true; |
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| 180 | } else { |
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| 181 | throw new \PEAR_Exception('invalid null handling option expecting: ' . |
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| 182 | 'STATS_REJECT_NULL, STATS_IGNORE_NULL or STATS_USE_NULL_AS_ZERO'); |
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| 183 | } |
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| 184 | } |
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| 185 | |||
| 186 | /** |
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| 187 | * Transforms the data by substracting each entry from the mean and |
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| 188 | * dividing by its standard deviation. This will reset all pre-calculated |
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| 189 | * values to their original (unset) defaults. |
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| 190 | * |
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| 191 | * @access public |
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| 192 | * @return mixed true on success, a PEAR_Error object otherwise |
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| 193 | * @see mean() |
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| 194 | * @see stDev() |
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| 195 | * @see setData() |
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| 196 | */ |
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| 197 | public function studentize() |
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| 198 | { |
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| 199 | try { |
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| 200 | $mean = $this->mean(); |
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| 201 | } catch (\PEAR_Exception $e) { |
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| 202 | return $mean; |
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| 203 | } |
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| 204 | try { |
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| 205 | $std = $this->stDev(); |
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| 206 | } catch (\PEAR_Exception $e) { |
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| 207 | return $std; |
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| 208 | } |
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| 209 | if ($std == 0) { |
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| 210 | throw new \PEAR_Exception('cannot studentize data, standard deviation is zero.'); |
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| 211 | } |
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| 212 | $arr = array(); |
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| 213 | if ($this->_dataOption == self::STATS_DATA_CUMMULATIVE) { |
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| 214 | foreach ($this->_data as $val => $freq) { |
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| 215 | $newval = ($val - $mean) / $std; |
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| 216 | $arr["$newval"] = $freq; |
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| 217 | } |
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| 218 | } else { |
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| 219 | foreach ($this->_data as $val) { |
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| 220 | $newval = ($val - $mean) / $std; |
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| 221 | $arr[] = $newval; |
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| 222 | } |
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| 223 | } |
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| 224 | return $this->setData($arr, $this->_dataOption); |
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| 225 | } |
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| 226 | |||
| 227 | /** |
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| 228 | * Transforms the data by substracting each entry from the mean. |
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| 229 | * This will reset all pre-calculated values to their original (unset) defaults. |
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| 230 | * |
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| 231 | * @access public |
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| 232 | * @return mixed true on success, a PEAR_Error object otherwise |
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| 233 | * @see mean() |
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| 234 | * @see setData() |
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| 235 | */ |
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| 236 | public function center() |
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| 237 | { |
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| 238 | try { |
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| 239 | $mean = $this->mean(); |
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| 240 | } catch (\PEAR_Exception $e) { |
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| 241 | return $mean; |
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| 242 | } |
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| 243 | $arr = array(); |
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| 244 | if ($this->_dataOption == self::STATS_DATA_CUMMULATIVE) { |
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| 245 | foreach ($this->_data as $val => $freq) { |
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| 246 | $newval = $val - $mean; |
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| 247 | $arr["$newval"] = $freq; |
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| 248 | } |
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| 249 | } else { |
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| 250 | foreach ($this->_data as $val) { |
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| 251 | $newval = $val - $mean; |
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| 252 | $arr[] = $newval; |
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| 253 | } |
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| 254 | } |
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| 255 | return $this->setData($arr, $this->_dataOption); |
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| 256 | } |
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| 257 | |||
| 258 | /** |
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| 259 | * Calculates the basic or full statistics for the data set |
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| 260 | * |
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| 261 | * @access public |
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| 262 | * @param int $mode one of STATS_BASIC or STATS_FULL |
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| 263 | * @param boolean $returnErrorObject whether the raw PEAR_Error (when true, default), |
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| 264 | * or only the error message will be returned (when false), if an error happens. |
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| 265 | * @return mixed an associative array of statistics on success, a PEAR_Error object otherwise |
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| 266 | * @see calcBasic() |
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| 267 | * @see calcFull() |
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| 268 | */ |
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| 269 | public function calc($mode, $returnErrorObject = true) |
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| 270 | { |
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| 271 | if ($this->_data == null) { |
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| 272 | throw new \PEAR_Exception('data has not been set'); |
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| 273 | } |
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| 274 | |||
| 275 | if ($mode == self::STATS_BASIC) { |
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| 276 | return $this->calcBasic($returnErrorObject); |
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| 277 | } elseif ($mode == self::STATS_FULL) { |
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| 278 | return $this->calcFull($returnErrorObject); |
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| 279 | } else { |
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| 280 | throw new \PEAR_Exception('incorrect mode, expected STATS_BASIC or STATS_FULL'); |
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| 281 | } |
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| 282 | } |
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| 283 | |||
| 284 | /** |
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| 285 | * Calculates a basic set of statistics |
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| 286 | * |
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| 287 | * @access public |
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| 288 | * @param boolean $returnErrorObject whether the raw PEAR_Error (when true, default), |
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| 289 | * or only the error message will be returned (when false), if an error happens. |
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| 290 | * @return mixed an associative array of statistics on success, a PEAR_Error object otherwise |
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| 291 | * @see calc() |
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| 292 | * @see calcFull() |
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| 293 | */ |
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| 294 | public function calcBasic($returnErrorObject = true) |
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| 295 | { |
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| 296 | return array( |
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| 297 | 'min' => $this->__format($this->min(), $returnErrorObject), |
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| 298 | 'max' => $this->__format($this->max(), $returnErrorObject), |
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| 299 | 'sum' => $this->__format($this->sum(), $returnErrorObject), |
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| 300 | 'sum2' => $this->__format($this->sum2(), $returnErrorObject), |
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| 301 | 'count' => $this->__format($this->count(), $returnErrorObject), |
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| 302 | 'mean' => $this->__format($this->mean(), $returnErrorObject), |
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| 303 | 'stdev' => $this->__format($this->stDev(), $returnErrorObject), |
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| 304 | 'variance' => $this->__format($this->variance(), $returnErrorObject), |
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| 305 | 'range' => $this->__format($this->range(), $returnErrorObject), |
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| 306 | ); |
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| 307 | } |
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| 308 | |||
| 309 | /** |
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| 310 | * Calculates a full set of statistics |
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| 311 | * |
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| 312 | * @access public |
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| 313 | * @param boolean $returnErrorObject whether the raw PEAR_Error (when true, default), |
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| 314 | * or only the error message will be returned (when false), if an error happens. |
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| 315 | * @return mixed an associative array of statistics on success, a PEAR_Error object otherwise |
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| 316 | * @see calc() |
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| 317 | * @see calcBasic() |
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| 318 | */ |
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| 319 | public function calcFull($returnErrorObject = true) |
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| 320 | { |
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| 321 | return array( |
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| 322 | 'min' => $this->__format($this->min(), $returnErrorObject), |
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| 323 | 'max' => $this->__format($this->max(), $returnErrorObject), |
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| 324 | 'sum' => $this->__format($this->sum(), $returnErrorObject), |
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| 325 | 'sum2' => $this->__format($this->sum2(), $returnErrorObject), |
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| 326 | 'count' => $this->__format($this->count(), $returnErrorObject), |
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| 327 | 'mean' => $this->__format($this->mean(), $returnErrorObject), |
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| 328 | 'median' => $this->__format($this->median(), $returnErrorObject), |
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| 329 | 'mode' => $this->__format($this->mode(), $returnErrorObject), |
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| 330 | 'midrange' => $this->__format($this->midrange(), $returnErrorObject), |
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| 331 | 'geometric_mean' => $this->__format($this->geometricMean(), $returnErrorObject), |
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| 332 | 'harmonic_mean' => $this->__format($this->harmonicMean(), $returnErrorObject), |
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| 333 | 'stdev' => $this->__format($this->stDev(), $returnErrorObject), |
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| 334 | 'absdev' => $this->__format($this->absDev(), $returnErrorObject), |
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| 335 | 'variance' => $this->__format($this->variance(), $returnErrorObject), |
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| 336 | 'range' => $this->__format($this->range(), $returnErrorObject), |
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| 337 | 'std_error_of_mean' => $this->__format($this->stdErrorOfMean(), $returnErrorObject), |
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| 338 | 'skewness' => $this->__format($this->skewness(), $returnErrorObject), |
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| 339 | 'kurtosis' => $this->__format($this->kurtosis(), $returnErrorObject), |
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| 340 | 'coeff_of_variation' => $this->__format($this->coeffOfVariation(), $returnErrorObject), |
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| 341 | 'sample_central_moments' => array( |
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| 342 | 1 => $this->__format($this->sampleCentralMoment(1), $returnErrorObject), |
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| 343 | 2 => $this->__format($this->sampleCentralMoment(2), $returnErrorObject), |
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| 344 | 3 => $this->__format($this->sampleCentralMoment(3), $returnErrorObject), |
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| 345 | 4 => $this->__format($this->sampleCentralMoment(4), $returnErrorObject), |
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| 346 | 5 => $this->__format($this->sampleCentralMoment(5), $returnErrorObject), |
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| 347 | ), |
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| 348 | 'sample_raw_moments' => array( |
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| 349 | 1 => $this->__format($this->sampleRawMoment(1), $returnErrorObject), |
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| 350 | 2 => $this->__format($this->sampleRawMoment(2), $returnErrorObject), |
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| 351 | 3 => $this->__format($this->sampleRawMoment(3), $returnErrorObject), |
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| 352 | 4 => $this->__format($this->sampleRawMoment(4), $returnErrorObject), |
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| 353 | 5 => $this->__format($this->sampleRawMoment(5), $returnErrorObject), |
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| 354 | ), |
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| 355 | 'frequency' => $this->__format($this->frequency(), $returnErrorObject), |
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| 356 | 'quartiles' => $this->__format($this->quartiles(), $returnErrorObject), |
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| 357 | 'interquartile_range' => $this->__format($this->interquartileRange(), $returnErrorObject), |
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| 358 | 'interquartile_mean' => $this->__format($this->interquartileMean(), $returnErrorObject), |
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| 359 | 'quartile_deviation' => $this->__format($this->quartileDeviation(), $returnErrorObject), |
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| 360 | 'quartile_variation_coefficient' => $this->__format($this->quartileVariationCoefficient(), $returnErrorObject), |
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| 361 | 'quartile_skewness_coefficient' => $this->__format($this->quartileSkewnessCoefficient(), $returnErrorObject), |
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| 362 | ); |
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| 363 | } |
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| 364 | |||
| 365 | /** |
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| 366 | * Calculates the minimum of a data set. |
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| 367 | * Handles cummulative data sets correctly$this->_data[0] |
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| 368 | * |
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| 369 | * @access public |
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| 370 | * @return mixed the minimum value on success, a PEAR_Error object otherwise |
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| 371 | * @see calc() |
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| 372 | * @see max() |
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| 373 | */ |
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| 374 | public function min() |
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| 375 | { |
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| 376 | if ($this->_data == null) { |
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| 377 | throw new \PEAR_Exception('data has not been set'); |
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| 378 | } |
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| 379 | |||
| 380 | if (!array_key_exists('min', $this->_calculatedValues)) { |
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| 381 | if ($this->_dataOption == self::STATS_DATA_CUMMULATIVE) { |
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| 382 | $min = min(array_keys($this->_data)); |
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| 383 | } else { |
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| 384 | $min = min($this->_data); |
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| 385 | } |
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| 386 | |||
| 387 | $this->_calculatedValues['min'] = $min; |
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| 388 | } |
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| 389 | |||
| 390 | return $this->_calculatedValues['min']; |
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| 391 | } |
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| 392 | |||
| 393 | /** |
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| 394 | * Calculates the maximum of a data set. |
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| 395 | * Handles cummulative data sets correctly |
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| 396 | * |
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| 397 | * @access public |
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| 398 | * @return mixed the maximum value on success, a PEAR_Error object otherwise |
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| 399 | * @see calc() |
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| 400 | * @see min() |
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| 401 | */ |
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| 402 | public function max() |
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| 403 | { |
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| 404 | if ($this->_data == null) { |
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| 405 | throw new \PEAR_Exception('data has not been set'); |
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| 406 | } |
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| 407 | if (!array_key_exists('max', $this->_calculatedValues)) { |
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| 408 | if ($this->_dataOption == self::STATS_DATA_CUMMULATIVE) { |
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| 409 | $max = max(array_keys($this->_data)); |
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| 410 | } else { |
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| 411 | $max = max($this->_data); |
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| 412 | } |
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| 413 | $this->_calculatedValues['max'] = $max; |
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| 414 | } |
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| 415 | return $this->_calculatedValues['max']; |
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| 416 | } |
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| 417 | |||
| 418 | /** |
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| 419 | * Calculates SUM { xi } |
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| 420 | * Handles cummulative data sets correctly |
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| 421 | * |
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| 422 | * @access public |
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| 423 | * @return mixed the sum on success, a PEAR_Error object otherwise |
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| 424 | * @see calc() |
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| 425 | * @see sum2() |
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| 426 | * @see sumN() |
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| 427 | */ |
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| 428 | public function sum() |
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| 429 | { |
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| 430 | if (!array_key_exists('sum', $this->_calculatedValues)) { |
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| 431 | try { |
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| 432 | $sum = $this->sumN(1); |
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| 433 | $this->_calculatedValues['sum'] = $sum; |
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| 434 | } catch (\PEAR_Exception $e) { |
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| 435 | return $sum; |
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| 436 | } |
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| 437 | } |
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| 438 | return $this->_calculatedValues['sum']; |
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| 439 | } |
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| 440 | |||
| 441 | /** |
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| 442 | * Calculates SUM { (xi)^2 } |
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| 443 | * Handles cummulative data sets correctly |
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| 444 | * |
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| 445 | * @access public |
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| 446 | * @return mixed the sum on success, a PEAR_Error object otherwise |
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| 447 | * @see calc() |
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| 448 | * @see sum() |
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| 449 | * @see sumN() |
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| 450 | */ |
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| 451 | public function sum2() |
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| 452 | { |
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| 453 | if (!array_key_exists('sum2', $this->_calculatedValues)) { |
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| 454 | try { |
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| 455 | $sum2 = $this->sumN(2); |
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| 456 | $this->_calculatedValues['sum2'] = $sum2; |
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| 457 | } catch (\PEAR_Exception $e) { |
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| 458 | return $sum2; |
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| 459 | } |
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| 460 | } |
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| 461 | return $this->_calculatedValues['sum2']; |
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| 462 | } |
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| 463 | |||
| 464 | /** |
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| 465 | * Calculates SUM { (xi)^n } |
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| 466 | * Handles cummulative data sets correctly |
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| 467 | * |
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| 468 | * @access public |
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| 469 | * @param numeric $n the exponent |
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| 470 | * @return mixed the sum on success, a PEAR_Error object otherwise |
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| 471 | * @see calc() |
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| 472 | * @see sum() |
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| 473 | * @see sum2() |
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| 474 | */ |
||
| 475 | public function sumN($n) |
||
| 476 | { |
||
| 477 | if ($this->_data == null) { |
||
| 478 | throw new \PEAR_Exception('data has not been set'); |
||
| 479 | } |
||
| 480 | $sumN = 0; |
||
| 481 | if ($this->_dataOption == self::STATS_DATA_CUMMULATIVE) { |
||
| 482 | foreach ($this->_data as $val => $freq) { |
||
| 483 | $sumN += $freq * pow((double) $val, (double) $n); |
||
| 484 | } |
||
| 485 | } else { |
||
| 486 | foreach ($this->_data as $val) { |
||
| 487 | $sumN += pow((double) $val, (double) $n); |
||
| 488 | } |
||
| 489 | } |
||
| 490 | return $sumN; |
||
| 491 | } |
||
| 492 | |||
| 493 | /** |
||
| 494 | * Calculates PROD { (xi) }, (the product of all observations) |
||
| 495 | * Handles cummulative data sets correctly |
||
| 496 | * |
||
| 497 | * @access public |
||
| 498 | * @return numeric|array|PEAR_Error the product as a number or an array of numbers |
||
| 499 | * (if there is numeric overflow) on success, |
||
| 500 | * a PEAR_Error object otherwise |
||
| 501 | * @see productN() |
||
| 502 | */ |
||
| 503 | public function product() |
||
| 504 | { |
||
| 505 | if (!array_key_exists('product', $this->_calculatedValues)) { |
||
| 506 | try { |
||
| 507 | $product = $this->productN(1); |
||
| 508 | $this->_calculatedValues['product'] = $product; |
||
| 509 | } catch (\PEAR_Exception $e) { |
||
| 510 | return $product; |
||
| 511 | } |
||
| 512 | } |
||
| 513 | return $this->_calculatedValues['product']; |
||
| 514 | } |
||
| 515 | |||
| 516 | /** |
||
| 517 | * Calculates PROD { (xi)^n }, which is the product of all observations |
||
| 518 | * Handles cummulative data sets correctly |
||
| 519 | * |
||
| 520 | * @access public |
||
| 521 | * @param numeric $n the exponent |
||
| 522 | * @return numeric|array|PEAR_Error the product as a number or an array of numbers |
||
| 523 | * (if there is numeric overflow) on success, |
||
| 524 | * a PEAR_Error object otherwise |
||
| 525 | * @see product() |
||
| 526 | */ |
||
| 527 | public function productN($n) |
||
| 528 | { |
||
| 529 | if ($this->_data == null) { |
||
| 530 | throw new \PEAR_Exception('data has not been set'); |
||
| 531 | } |
||
| 532 | $prodN = 1.0; |
||
| 533 | $partial = array(); |
||
| 534 | if ($this->_dataOption == self::STATS_DATA_CUMMULATIVE) { |
||
| 535 | foreach ($this->_data as $val => $freq) { |
||
| 536 | if ($val == 0) { |
||
| 537 | return 0.0; |
||
| 538 | } |
||
| 539 | $prodN *= $freq * pow((double) $val, (double) $n); |
||
| 540 | if ($prodN > 10000 * $n) { |
||
| 541 | $partial[] = $prodN; |
||
| 542 | $prodN = 1.0; |
||
| 543 | } |
||
| 544 | } |
||
| 545 | } else { |
||
| 546 | foreach ($this->_data as $val) { |
||
| 547 | if ($val == 0) { |
||
| 548 | return 0.0; |
||
| 549 | } |
||
| 550 | $prodN *= pow((double) $val, (double) $n); |
||
| 551 | if ($prodN > 10 * $n) { |
||
| 552 | $partial[] = $prodN; |
||
| 553 | $prodN = 1.0; |
||
| 554 | } |
||
| 555 | } |
||
| 556 | } |
||
| 557 | if (!empty($partial)) { |
||
| 558 | $partial[] = $prodN; |
||
| 559 | // try to reduce to a single value |
||
| 560 | $tmp = 1.0; |
||
| 561 | foreach ($partial as $val) { |
||
| 562 | $tmp *= $val; |
||
| 563 | // cannot reduce, return an array |
||
| 564 | if (is_infinite($tmp)) { |
||
| 565 | return $partial; |
||
| 566 | } |
||
| 567 | } |
||
| 568 | return $tmp; |
||
| 569 | } else { |
||
| 570 | return $prodN; |
||
| 571 | } |
||
| 572 | } |
||
| 573 | |||
| 574 | /** |
||
| 575 | * Calculates the number of data points in the set |
||
| 576 | * Handles cummulative data sets correctly |
||
| 577 | * |
||
| 578 | * @access public |
||
| 579 | * @return mixed the count on success, a PEAR_Error object otherwise |
||
| 580 | * @see calc() |
||
| 581 | */ |
||
| 582 | public function count() |
||
| 583 | { |
||
| 584 | if ($this->_data == null) { |
||
| 585 | throw new \PEAR_Exception('data has not been set'); |
||
| 586 | } |
||
| 587 | if (!array_key_exists('count', $this->_calculatedValues)) { |
||
| 588 | if ($this->_dataOption == self::STATS_DATA_CUMMULATIVE) { |
||
| 589 | $count = count($this->_dataExpanded); |
||
| 590 | } else { |
||
| 591 | $count = count($this->_data); |
||
| 592 | } |
||
| 593 | $this->_calculatedValues['count'] = $count; |
||
| 594 | } |
||
| 595 | return $this->_calculatedValues['count']; |
||
| 596 | } |
||
| 597 | |||
| 598 | /** |
||
| 599 | * Calculates the mean (average) of the data points in the set |
||
| 600 | * Handles cummulative data sets correctly |
||
| 601 | * |
||
| 602 | * @access public |
||
| 603 | * @return mixed the mean value on success, a PEAR_Error object otherwise |
||
| 604 | * @see calc() |
||
| 605 | * @see sum() |
||
| 606 | * @see count() |
||
| 607 | */ |
||
| 608 | public function mean() |
||
| 609 | { |
||
| 610 | if (!array_key_exists('mean', $this->_calculatedValues)) { |
||
| 611 | try { |
||
| 612 | $sum = $this->sum(); |
||
| 613 | try { |
||
| 614 | $count = $this->count(); |
||
| 615 | } catch (\PEAR_Exception $e) { |
||
| 616 | return $count; |
||
| 617 | } |
||
| 618 | $this->_calculatedValues['mean'] = $sum / $count; |
||
| 619 | } catch (\PEAR_Exception $e) { |
||
| 620 | return $sum; |
||
| 621 | } |
||
| 622 | } |
||
| 623 | return $this->_calculatedValues['mean']; |
||
| 624 | } |
||
| 625 | |||
| 626 | /** |
||
| 627 | * Calculates the range of the data set = max - min |
||
| 628 | * |
||
| 629 | * @access public |
||
| 630 | * @return mixed the value of the range on success, a PEAR_Error object otherwise. |
||
| 631 | */ |
||
| 632 | public function range() |
||
| 633 | { |
||
| 634 | if (!array_key_exists('range', $this->_calculatedValues)) { |
||
| 635 | try { |
||
| 636 | $min = $this->min(); |
||
| 637 | try { |
||
| 638 | $max = $this->max(); |
||
| 639 | } catch (\PEAR_Exception $e) { |
||
| 640 | return $max; |
||
| 641 | } |
||
| 642 | $this->_calculatedValues['range'] = $max - $min; |
||
| 643 | } catch (\PEAR_Exception $e) { |
||
| 644 | return $min; |
||
| 645 | } |
||
| 646 | } |
||
| 647 | return $this->_calculatedValues['range']; |
||
| 648 | } |
||
| 649 | |||
| 650 | /** |
||
| 651 | * Calculates the variance (unbiased) of the data points in the set |
||
| 652 | * Handles cummulative data sets correctly |
||
| 653 | * |
||
| 654 | * @access public |
||
| 655 | * @return mixed the variance value on success, a PEAR_Error object otherwise |
||
| 656 | * @see calc() |
||
| 657 | * @see __sumdiff() |
||
| 658 | * @see count() |
||
| 659 | */ |
||
| 660 | public function variance() |
||
| 661 | { |
||
| 662 | if (!array_key_exists('variance', $this->_calculatedValues)) { |
||
| 663 | try { |
||
| 664 | $variance = $this->__calcVariance(); |
||
| 665 | } catch (\PEAR_Exception $e) { |
||
| 666 | return $variance; |
||
| 667 | } |
||
| 668 | |||
| 669 | $this->_calculatedValues['variance'] = $variance; |
||
| 670 | } |
||
| 671 | return $this->_calculatedValues['variance']; |
||
| 672 | } |
||
| 673 | |||
| 674 | /** |
||
| 675 | * Calculates the standard deviation (unbiased) of the data points in the set |
||
| 676 | * Handles cummulative data sets correctly |
||
| 677 | * |
||
| 678 | * @access public |
||
| 679 | * @return mixed the standard deviation on success, a PEAR_Error object otherwise |
||
| 680 | * @see calc() |
||
| 681 | * @see variance() |
||
| 682 | */ |
||
| 683 | public function stDev() |
||
| 684 | { |
||
| 685 | if (!array_key_exists('stDev', $this->_calculatedValues)) { |
||
| 686 | try { |
||
| 687 | $variance = $this->variance(); |
||
| 688 | } catch (\PEAR_Exception $e) { |
||
| 689 | return $variance; |
||
| 690 | } |
||
| 691 | |||
| 692 | $this->_calculatedValues['stDev'] = sqrt($variance); |
||
| 693 | } |
||
| 694 | return $this->_calculatedValues['stDev']; |
||
| 695 | } |
||
| 696 | |||
| 697 | /** |
||
| 698 | * Calculates the variance (unbiased) of the data points in the set |
||
| 699 | * given a fixed mean (average) value. Not used in calcBasic(), calcFull() |
||
| 700 | * or calc(). |
||
| 701 | * Handles cummulative data sets correctly |
||
| 702 | * |
||
| 703 | * @access public |
||
| 704 | * @param numeric $mean the fixed mean value |
||
| 705 | * @return mixed the variance on success, a PEAR_Error object otherwise |
||
| 706 | * @see __sumdiff() |
||
| 707 | * @see count() |
||
| 708 | * @see variance() |
||
| 709 | */ |
||
| 710 | public function varianceWithMean($mean) |
||
| 711 | { |
||
| 712 | return $this->__calcVariance($mean); |
||
| 713 | } |
||
| 714 | |||
| 715 | /** |
||
| 716 | * Calculates the standard deviation (unbiased) of the data points in the set |
||
| 717 | * given a fixed mean (average) value. Not used in calcBasic(), calcFull() |
||
| 718 | * or calc(). |
||
| 719 | * Handles cummulative data sets correctly |
||
| 720 | * |
||
| 721 | * @access public |
||
| 722 | * @param numeric $mean the fixed mean value |
||
| 723 | * @return mixed the standard deviation on success, a PEAR_Error object otherwise |
||
| 724 | * @see varianceWithMean() |
||
| 725 | * @see stDev() |
||
| 726 | */ |
||
| 727 | public function stDevWithMean($mean) |
||
| 728 | { |
||
| 729 | try { |
||
| 730 | $varianceWM = $this->varianceWithMean($mean); |
||
| 731 | } catch (\PEAR_Exception $e) { |
||
| 732 | return $varianceWM; |
||
| 733 | } |
||
| 734 | |||
| 735 | return sqrt($varianceWM); |
||
| 736 | } |
||
| 737 | |||
| 738 | /** |
||
| 739 | * Calculates the absolute deviation of the data points in the set |
||
| 740 | * Handles cummulative data sets correctly |
||
| 741 | * |
||
| 742 | * @access public |
||
| 743 | * @return mixed the absolute deviation on success, a PEAR_Error object otherwise |
||
| 744 | * @see calc() |
||
| 745 | * @see __sumabsdev() |
||
| 746 | * @see count() |
||
| 747 | * @see absDevWithMean() |
||
| 748 | */ |
||
| 749 | public function absDev() |
||
| 750 | { |
||
| 751 | if (!array_key_exists('absDev', $this->_calculatedValues)) { |
||
| 752 | try { |
||
| 753 | $absDev = $this->__calcAbsoluteDeviation(); |
||
| 754 | } catch (\PEAR_Exception $e) { |
||
| 755 | return $absDev; |
||
| 756 | } |
||
| 757 | |||
| 758 | $this->_calculatedValues['absDev'] = $absDev; |
||
| 759 | } |
||
| 760 | return $this->_calculatedValues['absDev']; |
||
| 761 | } |
||
| 762 | |||
| 763 | /** |
||
| 764 | * Calculates the absolute deviation of the data points in the set |
||
| 765 | * given a fixed mean (average) value. Not used in calcBasic(), calcFull() |
||
| 766 | * or calc(). |
||
| 767 | * Handles cummulative data sets correctly |
||
| 768 | * |
||
| 769 | * @access public |
||
| 770 | * @param numeric $mean the fixed mean value |
||
| 771 | * @return mixed the absolute deviation on success, a PEAR_Error object otherwise |
||
| 772 | * @see __sumabsdev() |
||
| 773 | * @see absDev() |
||
| 774 | */ |
||
| 775 | public function absDevWithMean($mean) |
||
| 776 | { |
||
| 777 | return $this->__calcAbsoluteDeviation($mean); |
||
| 778 | } |
||
| 779 | |||
| 780 | /** |
||
| 781 | * Calculates the skewness of the data distribution in the set |
||
| 782 | * The skewness measures the degree of asymmetry of a distribution, |
||
| 783 | * and is related to the third central moment of a distribution. |
||
| 784 | * A normal distribution has a skewness = 0 |
||
| 785 | * A distribution with a tail off towards the high end of the scale |
||
| 786 | * (positive skew) has a skewness > 0 |
||
| 787 | * A distribution with a tail off towards the low end of the scale |
||
| 788 | * (negative skew) has a skewness < 0 |
||
| 789 | * Handles cummulative data sets correctly |
||
| 790 | * |
||
| 791 | * @access public |
||
| 792 | * @return mixed the skewness value on success, a PEAR_Error object otherwise |
||
| 793 | * @see __sumdiff() |
||
| 794 | * @see count() |
||
| 795 | * @see stDev() |
||
| 796 | * @see calc() |
||
| 797 | */ |
||
| 798 | public function skewness() |
||
| 799 | { |
||
| 800 | if (!array_key_exists('skewness', $this->_calculatedValues)) { |
||
| 801 | try { |
||
| 802 | $count = $this->count(); |
||
| 803 | try { |
||
| 804 | $stDev = $this->stDev(); |
||
| 805 | try { |
||
| 806 | $sumdiff3 = $this->__sumdiff(3); |
||
| 807 | } catch (\PEAR_Exception $e) { |
||
| 808 | return $sumdiff3; |
||
| 809 | } |
||
| 810 | } catch (\PEAR_Exception $e) { |
||
| 811 | return $stDev; |
||
| 812 | } |
||
| 813 | } catch (\PEAR_Exception $e) { |
||
| 814 | return $count; |
||
| 815 | } |
||
| 816 | |||
| 817 | $this->_calculatedValues['skewness'] = ($sumdiff3 / ($count * pow($stDev, 3))); |
||
| 818 | } |
||
| 819 | return $this->_calculatedValues['skewness']; |
||
| 820 | } |
||
| 821 | |||
| 822 | /** |
||
| 823 | * Calculates the kurtosis of the data distribution in the set |
||
| 824 | * The kurtosis measures the degrees of peakedness of a distribution. |
||
| 825 | * It is also called the "excess" or "excess coefficient", and is |
||
| 826 | * a normalized form of the fourth central moment of a distribution. |
||
| 827 | * A normal distributions has kurtosis = 0 |
||
| 828 | * A narrow and peaked (leptokurtic) distribution has a |
||
| 829 | * kurtosis > 0 |
||
| 830 | * A flat and wide (platykurtic) distribution has a kurtosis < 0 |
||
| 831 | * Handles cummulative data sets correctly |
||
| 832 | * |
||
| 833 | * @access public |
||
| 834 | * @return mixed the kurtosis value on success, a PEAR_Error object otherwise |
||
| 835 | * @see __sumdiff() |
||
| 836 | * @see count() |
||
| 837 | * @see stDev() |
||
| 838 | * @see calc() |
||
| 839 | */ |
||
| 840 | public function kurtosis() |
||
| 841 | { |
||
| 842 | if (!array_key_exists('kurtosis', $this->_calculatedValues)) { |
||
| 843 | try { |
||
| 844 | $count = $this->count(); |
||
| 845 | try { |
||
| 846 | $stDev = $this->stDev(); |
||
| 847 | try { |
||
| 848 | $sumdiff4 = $this->__sumdiff(4); |
||
| 849 | } catch (\PEAR_Exception $e) { |
||
| 850 | return $sumdiff4; |
||
| 851 | } |
||
| 852 | } catch (\PEAR_Exception $e) { |
||
| 853 | return $stDev; |
||
| 854 | } |
||
| 855 | } catch (\PEAR_Exception $e) { |
||
| 856 | return $count; |
||
| 857 | } |
||
| 858 | |||
| 859 | $this->_calculatedValues['kurtosis'] = ($sumdiff4 / ($count * pow($stDev, 4))) - 3; |
||
| 860 | } |
||
| 861 | return $this->_calculatedValues['kurtosis']; |
||
| 862 | } |
||
| 863 | |||
| 864 | /** |
||
| 865 | * Calculates the median of a data set. |
||
| 866 | * The median is the value such that half of the points are below it |
||
| 867 | * in a sorted data set. |
||
| 868 | * If the number of values is odd, it is the middle item. |
||
| 869 | * If the number of values is even, is the average of the two middle items. |
||
| 870 | * Handles cummulative data sets correctly |
||
| 871 | * |
||
| 872 | * @access public |
||
| 873 | * @return mixed the median value on success, a PEAR_Error object otherwise |
||
| 874 | * @see count() |
||
| 875 | * @see calc() |
||
| 876 | */ |
||
| 877 | public function median() |
||
| 878 | { |
||
| 879 | if ($this->_data == null) { |
||
| 880 | throw new \PEAR_Exception('data has not been set'); |
||
| 881 | } |
||
| 882 | if (!array_key_exists('median', $this->_calculatedValues)) { |
||
| 883 | if ($this->_dataOption == self::STATS_DATA_CUMMULATIVE) { |
||
| 884 | $arr = &$this->_dataExpanded; |
||
| 885 | } else { |
||
| 886 | $arr = &$this->_data; |
||
| 887 | } |
||
| 888 | try { |
||
| 889 | $n = $this->count(); |
||
| 890 | } catch (\PEAR_Exception $e) { |
||
| 891 | return $n; |
||
| 892 | } |
||
| 893 | |||
| 894 | $h = intval($n / 2); |
||
| 895 | if ($n % 2 == 0) { |
||
| 896 | $median = ($arr[$h] + $arr[$h - 1]) / 2; |
||
| 897 | } else { |
||
| 898 | $median = $arr[$h]; |
||
| 899 | } |
||
| 900 | $this->_calculatedValues['median'] = $median; |
||
| 901 | } |
||
| 902 | return $this->_calculatedValues['median']; |
||
| 903 | } |
||
| 904 | |||
| 905 | /** |
||
| 906 | * Calculates the mode of a data set. |
||
| 907 | * The mode is the value with the highest frequency in the data set. |
||
| 908 | * There can be more than one mode. |
||
| 909 | * Handles cummulative data sets correctly |
||
| 910 | * |
||
| 911 | * @access public |
||
| 912 | * @return mixed an array of mode value on success, a PEAR_Error object otherwise |
||
| 913 | * @see frequency() |
||
| 914 | * @see calc() |
||
| 915 | */ |
||
| 916 | public function mode() |
||
| 917 | { |
||
| 918 | if ($this->_data == null) { |
||
| 919 | throw new \PEAR_Exception('data has not been set'); |
||
| 920 | } |
||
| 921 | if (!array_key_exists('mode', $this->_calculatedValues)) { |
||
| 922 | if ($this->_dataOption == self::STATS_DATA_CUMMULATIVE) { |
||
| 923 | $arr = $this->_data; |
||
| 924 | } else { |
||
| 925 | $arr = $this->frequency(); |
||
| 926 | } |
||
| 927 | arsort($arr); |
||
| 928 | $mcount = 1; |
||
| 929 | foreach ($arr as $val => $freq) { |
||
| 930 | if ($mcount == 1) { |
||
| 931 | $mode = array($val); |
||
| 932 | $mfreq = $freq; |
||
| 933 | $mcount++; |
||
| 934 | continue; |
||
| 935 | } |
||
| 936 | if ($mfreq == $freq) { |
||
| 937 | $mode[] = $val; |
||
| 938 | } |
||
| 939 | |||
| 940 | if ($mfreq > $freq) { |
||
| 941 | break; |
||
| 942 | } |
||
| 943 | } |
||
| 944 | $this->_calculatedValues['mode'] = $mode; |
||
| 945 | } |
||
| 946 | return $this->_calculatedValues['mode']; |
||
| 947 | } |
||
| 948 | |||
| 949 | /** |
||
| 950 | * Calculates the midrange of a data set. |
||
| 951 | * The midrange is the average of the minimum and maximum of the data set. |
||
| 952 | * Handles cummulative data sets correctly |
||
| 953 | * |
||
| 954 | * @access public |
||
| 955 | * @return mixed the midrange value on success, a PEAR_Error object otherwise |
||
| 956 | * @see min() |
||
| 957 | * @see max() |
||
| 958 | * @see calc() |
||
| 959 | */ |
||
| 960 | public function midrange() |
||
| 961 | { |
||
| 962 | if (!array_key_exists('midrange', $this->_calculatedValues)) { |
||
| 963 | try { |
||
| 964 | $min = $this->min(); |
||
| 965 | try { |
||
| 966 | $max = $this->max(); |
||
| 967 | } catch (\PEAR_Exception $e) { |
||
| 968 | return $max; |
||
| 969 | } |
||
| 970 | } catch (\PEAR_Exception $e) { |
||
| 971 | return $min; |
||
| 972 | } |
||
| 973 | |||
| 974 | $this->_calculatedValues['midrange'] = (($max + $min) / 2); |
||
| 975 | } |
||
| 976 | return $this->_calculatedValues['midrange']; |
||
| 977 | } |
||
| 978 | |||
| 979 | /** |
||
| 980 | * Calculates the geometrical mean of the data points in the set |
||
| 981 | * Handles cummulative data sets correctly |
||
| 982 | * |
||
| 983 | * @access public |
||
| 984 | * @return mixed the geometrical mean value on success, a PEAR_Error object otherwise |
||
| 985 | * @see calc() |
||
| 986 | * @see product() |
||
| 987 | * @see count() |
||
| 988 | */ |
||
| 989 | public function geometricMean() |
||
| 990 | { |
||
| 991 | if (!array_key_exists('geometricMean', $this->_calculatedValues)) { |
||
| 992 | try { |
||
| 993 | $count = $this->count(); |
||
| 994 | } catch (\PEAR_Exception $e) { |
||
| 995 | return $count; |
||
| 996 | } |
||
| 997 | try { |
||
| 998 | $prod = $this->product(); |
||
| 999 | } catch (\PEAR_Exception $e) { |
||
| 1000 | return $prod; |
||
| 1001 | } |
||
| 1002 | if (is_array($prod)) { |
||
| 1003 | $geomMean = 1.0; |
||
| 1004 | foreach ($prod as $val) { |
||
| 1005 | $geomMean *= pow($val, 1 / $count); |
||
| 1006 | } |
||
| 1007 | $this->_calculatedValues['geometricMean'] = $geomMean; |
||
| 1008 | } else { |
||
| 1009 | if ($prod == 0.0) { |
||
| 1010 | return 0.0; |
||
| 1011 | } |
||
| 1012 | if ($prod < 0) { |
||
| 1013 | throw new \PEAR_Exception('The product of the data set is negative, geometric mean undefined.'); |
||
| 1014 | } |
||
| 1015 | $this->_calculatedValues['geometricMean'] = pow($prod, 1 / $count); |
||
| 1016 | } |
||
| 1017 | } |
||
| 1018 | return $this->_calculatedValues['geometricMean']; |
||
| 1019 | } |
||
| 1020 | |||
| 1021 | /** |
||
| 1022 | * Calculates the harmonic mean of the data points in the set |
||
| 1023 | * Handles cummulative data sets correctly |
||
| 1024 | * |
||
| 1025 | * @access public |
||
| 1026 | * @return mixed the harmonic mean value on success, a PEAR_Error object otherwise |
||
| 1027 | * @see calc() |
||
| 1028 | * @see count() |
||
| 1029 | */ |
||
| 1030 | public function harmonicMean() |
||
| 1031 | { |
||
| 1032 | if ($this->_data == null) { |
||
| 1033 | throw new \PEAR_Exception('data has not been set'); |
||
| 1034 | } |
||
| 1035 | if (!array_key_exists('harmonicMean', $this->_calculatedValues)) { |
||
| 1036 | try { |
||
| 1037 | $count = $this->count(); |
||
| 1038 | } catch (\PEAR_Exception $e) { |
||
| 1039 | return $count; |
||
| 1040 | } |
||
| 1041 | $invsum = 0.0; |
||
| 1042 | if ($this->_dataOption == self::STATS_DATA_CUMMULATIVE) { |
||
| 1043 | foreach ($this->_data as $val => $freq) { |
||
| 1044 | if ($val == 0) { |
||
| 1045 | throw new \PEAR_Exception('cannot calculate a ' . |
||
| 1046 | 'harmonic mean with data values of zero.'); |
||
| 1047 | } |
||
| 1048 | $invsum += $freq / $val; |
||
| 1049 | } |
||
| 1050 | } else { |
||
| 1051 | foreach ($this->_data as $val) { |
||
| 1052 | if ($val == 0) { |
||
| 1053 | throw new \PEAR_Exception('cannot calculate a ' . |
||
| 1054 | 'harmonic mean with data values of zero.'); |
||
| 1055 | } |
||
| 1056 | $invsum += 1 / $val; |
||
| 1057 | } |
||
| 1058 | } |
||
| 1059 | $this->_calculatedValues['harmonicMean'] = $count / $invsum; |
||
| 1060 | } |
||
| 1061 | return $this->_calculatedValues['harmonicMean']; |
||
| 1062 | } |
||
| 1063 | |||
| 1064 | /** |
||
| 1065 | * Calculates the nth central moment (m{n}) of a data set. |
||
| 1066 | * |
||
| 1067 | * The definition of a sample central moment is: |
||
| 1068 | * |
||
| 1069 | * m{n} = 1/N * SUM { (xi - avg)^n } |
||
| 1070 | * |
||
| 1071 | * where: N = sample size, avg = sample mean. |
||
| 1072 | * |
||
| 1073 | * @access public |
||
| 1074 | * @param integer $n moment to calculate |
||
| 1075 | * @return mixed the numeric value of the moment on success, PEAR_Error otherwise |
||
| 1076 | */ |
||
| 1077 | public function sampleCentralMoment($n) |
||
| 1078 | { |
||
| 1079 | if (!is_int($n) || $n < 1) { |
||
| 1080 | throw new \PEAR_Exception('moment must be a positive integer >= 1.'); |
||
| 1081 | } |
||
| 1082 | |||
| 1083 | if ($n == 1) { |
||
| 1084 | return 0; |
||
| 1085 | } |
||
| 1086 | try { |
||
| 1087 | $count = $this->count(); |
||
| 1088 | } catch (\PEAR_Exception $e) { |
||
| 1089 | return $count; |
||
| 1090 | } |
||
| 1091 | if ($count == 0) { |
||
| 1092 | throw new \PEAR_Exception("Cannot calculate {$n}th sample moment, " . |
||
| 1093 | 'there are zero data entries'); |
||
| 1094 | } |
||
| 1095 | try { |
||
| 1096 | $sum = $this->__sumdiff($n); |
||
| 1097 | } catch (\PEAR_Exception $e) { |
||
| 1098 | return $sum; |
||
| 1099 | } |
||
| 1100 | return ($sum / $count); |
||
| 1101 | } |
||
| 1102 | |||
| 1103 | /** |
||
| 1104 | * Calculates the nth raw moment (m{n}) of a data set. |
||
| 1105 | * |
||
| 1106 | * The definition of a sample central moment is: |
||
| 1107 | * |
||
| 1108 | * m{n} = 1/N * SUM { xi^n } |
||
| 1109 | * |
||
| 1110 | * where: N = sample size, avg = sample mean. |
||
| 1111 | * |
||
| 1112 | * @access public |
||
| 1113 | * @param integer $n moment to calculate |
||
| 1114 | * @return mixed the numeric value of the moment on success, PEAR_Error otherwise |
||
| 1115 | */ |
||
| 1116 | public function sampleRawMoment($n) |
||
| 1117 | { |
||
| 1118 | if (!is_int($n) || $n < 1) { |
||
| 1119 | throw new \PEAR_Exception('moment must be a positive integer >= 1.'); |
||
| 1120 | } |
||
| 1121 | |||
| 1122 | try { |
||
| 1123 | $count = $this->count(); |
||
| 1124 | } catch (\PEAR_Exception $e) { |
||
| 1125 | return $count; |
||
| 1126 | } |
||
| 1127 | if ($count == 0) { |
||
| 1128 | throw new \PEAR_Exception("Cannot calculate {$n}th raw moment, " . |
||
| 1129 | 'there are zero data entries.'); |
||
| 1130 | } |
||
| 1131 | try { |
||
| 1132 | $sum = $this->sumN($n); |
||
| 1133 | } catch (\PEAR_Exception $e) { |
||
| 1134 | return $sum; |
||
| 1135 | } |
||
| 1136 | return ($sum / $count); |
||
| 1137 | } |
||
| 1138 | |||
| 1139 | /** |
||
| 1140 | * Calculates the coefficient of variation of a data set. |
||
| 1141 | * The coefficient of variation measures the spread of a set of data |
||
| 1142 | * as a proportion of its mean. It is often expressed as a percentage. |
||
| 1143 | * Handles cummulative data sets correctly |
||
| 1144 | * |
||
| 1145 | * @access public |
||
| 1146 | * @return mixed the coefficient of variation on success, a PEAR_Error object otherwise |
||
| 1147 | * @see stDev() |
||
| 1148 | * @see mean() |
||
| 1149 | * @see calc() |
||
| 1150 | */ |
||
| 1151 | public function coeffOfVariation() |
||
| 1152 | { |
||
| 1153 | if (!array_key_exists('coeffOfVariation', $this->_calculatedValues)) { |
||
| 1154 | try { |
||
| 1155 | $mean = $this->mean(); |
||
| 1156 | } catch (\PEAR_Exception $e) { |
||
| 1157 | return $mean; |
||
| 1158 | } |
||
| 1159 | |||
| 1160 | if ($mean == 0.0) { |
||
| 1161 | throw new \PEAR_Exception('cannot calculate the coefficient ' . |
||
| 1162 | 'of variation, mean of sample is zero'); |
||
| 1163 | } |
||
| 1164 | try { |
||
| 1165 | $stDev = $this->stDev(); |
||
| 1166 | } catch (\PEAR_Exception $e) { |
||
| 1167 | return $stDev; |
||
| 1168 | } |
||
| 1169 | |||
| 1170 | $this->_calculatedValues['coeffOfVariation'] = $stDev / $mean; |
||
| 1171 | } |
||
| 1172 | return $this->_calculatedValues['coeffOfVariation']; |
||
| 1173 | } |
||
| 1174 | |||
| 1175 | /** |
||
| 1176 | * Calculates the standard error of the mean. |
||
| 1177 | * It is the standard deviation of the sampling distribution of |
||
| 1178 | * the mean. The formula is: |
||
| 1179 | * |
||
| 1180 | * S.E. Mean = SD / (N)^(1/2) |
||
| 1181 | * |
||
| 1182 | * This formula does not assume a normal distribution, and shows |
||
| 1183 | * that the size of the standard error of the mean is inversely |
||
| 1184 | * proportional to the square root of the sample size. |
||
| 1185 | * |
||
| 1186 | * @access public |
||
| 1187 | * @return mixed the standard error of the mean on success, a PEAR_Error object otherwise |
||
| 1188 | * @see stDev() |
||
| 1189 | * @see count() |
||
| 1190 | * @see calc() |
||
| 1191 | */ |
||
| 1192 | public function stdErrorOfMean() |
||
| 1193 | { |
||
| 1194 | if (!array_key_exists('stdErrorOfMean', $this->_calculatedValues)) { |
||
| 1195 | try { |
||
| 1196 | $count = $this->count(); |
||
| 1197 | } catch (\PEAR_Exception $e) { |
||
| 1198 | return $count; |
||
| 1199 | } |
||
| 1200 | try { |
||
| 1201 | $stDev = $this->stDev(); |
||
| 1202 | } catch (\PEAR_Exception $e) { |
||
| 1203 | return $stDev; |
||
| 1204 | } |
||
| 1205 | $this->_calculatedValues['stdErrorOfMean'] = $stDev / sqrt($count); |
||
| 1206 | } |
||
| 1207 | return $this->_calculatedValues['stdErrorOfMean']; |
||
| 1208 | } |
||
| 1209 | |||
| 1210 | /** |
||
| 1211 | * Calculates the value frequency table of a data set. |
||
| 1212 | * Handles cummulative data sets correctly |
||
| 1213 | * |
||
| 1214 | * @access public |
||
| 1215 | * @return mixed an associative array of value=>frequency items on success, a PEAR_Error object otherwise |
||
| 1216 | * @see min() |
||
| 1217 | * @see max() |
||
| 1218 | * @see calc() |
||
| 1219 | */ |
||
| 1220 | public function frequency() |
||
| 1221 | { |
||
| 1222 | if ($this->_data == null) { |
||
| 1223 | throw new \PEAR_Exception('data has not been set'); |
||
| 1224 | } |
||
| 1225 | if (!array_key_exists('frequency', $this->_calculatedValues)) { |
||
| 1226 | if ($this->_dataOption == self::STATS_DATA_CUMMULATIVE) { |
||
| 1227 | $freq = $this->_data; |
||
| 1228 | } else { |
||
| 1229 | $freq = array(); |
||
| 1230 | foreach ($this->_data as $val) { |
||
| 1231 | if (!isset($freq["$val"])) { |
||
| 1232 | $freq["$val"] = 0; |
||
| 1233 | } |
||
| 1234 | $freq["$val"]++; |
||
| 1235 | } |
||
| 1236 | ksort($freq); |
||
| 1237 | } |
||
| 1238 | $this->_calculatedValues['frequency'] = $freq; |
||
| 1239 | } |
||
| 1240 | return $this->_calculatedValues['frequency']; |
||
| 1241 | } |
||
| 1242 | |||
| 1243 | /** |
||
| 1244 | * The quartiles are defined as the values that divide a sorted |
||
| 1245 | * data set into four equal-sized subsets, and correspond to the |
||
| 1246 | * 25th, 50th, and 75th percentiles. |
||
| 1247 | * |
||
| 1248 | * @access public |
||
| 1249 | * @return mixed an associative array of quartiles on success, a PEAR_Error otherwise |
||
| 1250 | * @see percentile() |
||
| 1251 | */ |
||
| 1252 | public function quartiles() |
||
| 1253 | { |
||
| 1254 | if (!array_key_exists('quartiles', $this->_calculatedValues)) { |
||
| 1255 | try { |
||
| 1256 | $q1 = $this->percentile(25); |
||
| 1257 | try { |
||
| 1258 | $q2 = $this->percentile(50); |
||
| 1259 | try { |
||
| 1260 | $q3 = $this->percentile(75); |
||
| 1261 | } catch (\PEAR_Exception $e) { |
||
| 1262 | return $q3; |
||
| 1263 | } |
||
| 1264 | } catch (\PEAR_Exception $e) { |
||
| 1265 | return $q2; |
||
| 1266 | } |
||
| 1267 | } catch (\PEAR_Exception $e) { |
||
| 1268 | return $q1; |
||
| 1269 | } |
||
| 1270 | |||
| 1271 | $this->_calculatedValues['quartiles'] = array( |
||
| 1272 | '25' => $q1, |
||
| 1273 | '50' => $q2, |
||
| 1274 | '75' => $q3, |
||
| 1275 | ); |
||
| 1276 | } |
||
| 1277 | return $this->_calculatedValues['quartiles']; |
||
| 1278 | } |
||
| 1279 | |||
| 1280 | /** |
||
| 1281 | * The interquartile mean is defined as the mean of the values left |
||
| 1282 | * after discarding the lower 25% and top 25% ranked values, i.e.: |
||
| 1283 | * |
||
| 1284 | * interquart mean = mean(<P(25),P(75)>) |
||
| 1285 | * |
||
| 1286 | * where: P = percentile |
||
| 1287 | * |
||
| 1288 | * @todo need to double check the equation |
||
| 1289 | * @access public |
||
| 1290 | * @return mixed a numeric value on success, a PEAR_Error otherwise |
||
| 1291 | * @see quartiles() |
||
| 1292 | */ |
||
| 1293 | public function interquartileMean() |
||
| 1294 | { |
||
| 1295 | if (!array_key_exists('interquartileMean', $this->_calculatedValues)) { |
||
| 1296 | try { |
||
| 1297 | $quart = $this->quartiles(); |
||
| 1298 | } catch (\PEAR_Exception $e) { |
||
| 1299 | return $quart; |
||
| 1300 | } |
||
| 1301 | $q3 = $quart['75']; |
||
| 1302 | $q1 = $quart['25']; |
||
| 1303 | $sum = 0; |
||
| 1304 | $n = 0; |
||
| 1305 | foreach ($this->getData(true) as $val) { |
||
| 1306 | if ($val >= $q1 && $val <= $q3) { |
||
| 1307 | $sum += $val; |
||
| 1308 | $n++; |
||
| 1309 | } |
||
| 1310 | } |
||
| 1311 | if ($n == 0) { |
||
| 1312 | throw new \PEAR_Exception('error calculating interquartile mean, ' . |
||
| 1313 | 'empty interquartile range of values.'); |
||
| 1314 | } |
||
| 1315 | $this->_calculatedValues['interquartileMean'] = $sum / $n; |
||
| 1316 | } |
||
| 1317 | return $this->_calculatedValues['interquartileMean']; |
||
| 1318 | } |
||
| 1319 | |||
| 1320 | /** |
||
| 1321 | * The interquartile range is the distance between the 75th and 25th |
||
| 1322 | * percentiles. Basically the range of the middle 50% of the data set, |
||
| 1323 | * and thus is not affected by outliers or extreme values. |
||
| 1324 | * |
||
| 1325 | * interquart range = P(75) - P(25) |
||
| 1326 | * |
||
| 1327 | * where: P = percentile |
||
| 1328 | * |
||
| 1329 | * @access public |
||
| 1330 | * @return mixed a numeric value on success, a PEAR_Error otherwise |
||
| 1331 | * @see quartiles() |
||
| 1332 | */ |
||
| 1333 | public function interquartileRange() |
||
| 1346 | } |
||
| 1347 | |||
| 1348 | /** |
||
| 1349 | * The quartile deviation is half of the interquartile range value |
||
| 1350 | * |
||
| 1351 | * quart dev = (P(75) - P(25)) / 2 |
||
| 1352 | * |
||
| 1353 | * where: P = percentile |
||
| 1354 | * |
||
| 1355 | * @access public |
||
| 1356 | * @return mixed a numeric value on success, a PEAR_Error otherwise |
||
| 1357 | * @see quartiles() |
||
| 1358 | * @see interquartileRange() |
||
| 1359 | */ |
||
| 1360 | public function quartileDeviation() |
||
| 1361 | { |
||
| 1362 | if (!array_key_exists('quartileDeviation', $this->_calculatedValues)) { |
||
| 1363 | try { |
||
| 1364 | $iqr = $this->interquartileRange(); |
||
| 1365 | } catch (\PEAR_Exception $e) { |
||
| 1366 | return $iqr; |
||
| 1367 | } |
||
| 1368 | $this->_calculatedValues['quartileDeviation'] = $iqr / 2; |
||
| 1369 | } |
||
| 1370 | return $this->_calculatedValues['quartileDeviation']; |
||
| 1371 | } |
||
| 1372 | |||
| 1373 | /** |
||
| 1374 | * The quartile variation coefficient is defined as follows: |
||
| 1375 | * |
||
| 1376 | * quart var coeff = 100 * (P(75) - P(25)) / (P(75) + P(25)) |
||
| 1377 | * |
||
| 1378 | * where: P = percentile |
||
| 1379 | * |
||
| 1380 | * @todo need to double check the equation |
||
| 1381 | * @access public |
||
| 1382 | * @return mixed a numeric value on success, a PEAR_Error otherwise |
||
| 1383 | * @see quartiles() |
||
| 1384 | */ |
||
| 1385 | public function quartileVariationCoefficient() |
||
| 1400 | } |
||
| 1401 | |||
| 1402 | /** |
||
| 1403 | * The quartile skewness coefficient (also known as Bowley Skewness), |
||
| 1404 | * is defined as follows: |
||
| 1405 | * |
||
| 1406 | * quart skewness coeff = (P(25) - 2*P(50) + P(75)) / (P(75) - P(25)) |
||
| 1407 | * |
||
| 1408 | * where: P = percentile |
||
| 1409 | * |
||
| 1410 | * @todo need to double check the equation |
||
| 1411 | * @access public |
||
| 1412 | * @return mixed a numeric value on success, a PEAR_Error otherwise |
||
| 1413 | * @see quartiles() |
||
| 1414 | */ |
||
| 1415 | public function quartileSkewnessCoefficient() |
||
| 1416 | { |
||
| 1417 | if (!array_key_exists('quartileSkewnessCoefficient', $this->_calculatedValues)) { |
||
| 1418 | try { |
||
| 1419 | $quart = $this->quartiles(); |
||
| 1420 | } catch (\PEAR_Exception $e) { |
||
| 1421 | return $quart; |
||
| 1422 | } |
||
| 1423 | $q3 = $quart['75']; |
||
| 1424 | $q2 = $quart['50']; |
||
| 1425 | $q1 = $quart['25']; |
||
| 1426 | $d = $q3 - 2 * $q2 + $q1; |
||
| 1427 | $s = $q3 - $q1; |
||
| 1428 | $this->_calculatedValues['quartileSkewnessCoefficient'] = $d / $s; |
||
| 1429 | } |
||
| 1430 | return $this->_calculatedValues['quartileSkewnessCoefficient']; |
||
| 1431 | } |
||
| 1432 | |||
| 1433 | /** |
||
| 1434 | * The pth percentile is the value such that p% of the a sorted data set |
||
| 1435 | * is smaller than it, and (100 - p)% of the data is larger. |
||
| 1436 | * |
||
| 1437 | * A quick algorithm to pick the appropriate value from a sorted data |
||
| 1438 | * set is as follows: |
||
| 1439 | * |
||
| 1440 | * - Count the number of values: n |
||
| 1441 | * - Calculate the position of the value in the data list: i = p * (n + 1) |
||
| 1442 | * - if i is an integer, return the data at that position |
||
| 1443 | * - if i < 1, return the minimum of the data set |
||
| 1444 | * - if i > n, return the maximum of the data set |
||
| 1445 | * - otherwise, average the entries at adjacent positions to i |
||
| 1446 | * |
||
| 1447 | * The median is the 50th percentile value. |
||
| 1448 | * |
||
| 1449 | * @todo need to double check generality of the algorithm |
||
| 1450 | * |
||
| 1451 | * @access public |
||
| 1452 | * @param numeric $p the percentile to estimate, e.g. 25 for 25th percentile |
||
| 1453 | * @return mixed a numeric value on success, a PEAR_Error otherwise |
||
| 1454 | * @see quartiles() |
||
| 1455 | * @see median() |
||
| 1456 | */ |
||
| 1457 | public function percentile($p) |
||
| 1481 | } |
||
| 1482 | } |
||
| 1483 | |||
| 1484 | // private methods |
||
| 1485 | |||
| 1486 | /** |
||
| 1487 | * Utility function to calculate: SUM { (xi - mean)^n } |
||
| 1488 | * |
||
| 1489 | * @access private |
||
| 1490 | * @param numeric $power the exponent |
||
| 1491 | * @param optional double $mean the data set mean value |
||
| 1492 | * @return mixed the sum on success, a PEAR_Error object otherwise |
||
| 1493 | * |
||
| 1494 | * @see stDev() |
||
| 1495 | * @see variaceWithMean(); |
||
| 1496 | * @see skewness(); |
||
| 1497 | * @see kurtosis(); |
||
| 1498 | */ |
||
| 1499 | public function __sumdiff($power, $mean = null) |
||
| 1500 | { |
||
| 1501 | if ($this->_data == null) { |
||
| 1502 | throw new \PEAR_Exception('data has not been set'); |
||
| 1503 | } |
||
| 1504 | if (is_null($mean)) { |
||
| 1505 | try { |
||
| 1506 | $mean = $this->mean(); |
||
| 1507 | } catch (\PEAR_Exception $e) { |
||
| 1508 | return $mean; |
||
| 1509 | } |
||
| 1510 | } |
||
| 1511 | $sdiff = 0; |
||
| 1512 | if ($this->_dataOption == self::STATS_DATA_CUMMULATIVE) { |
||
| 1513 | foreach ($this->_data as $val => $freq) { |
||
| 1514 | $sdiff += $freq * pow((double) ($val - $mean), (double) $power); |
||
| 1515 | } |
||
| 1516 | } else { |
||
| 1517 | foreach ($this->_data as $val) { |
||
| 1518 | $sdiff += pow((double) ($val - $mean), (double) $power); |
||
| 1519 | } |
||
| 1520 | } |
||
| 1521 | return $sdiff; |
||
| 1522 | } |
||
| 1523 | |||
| 1524 | /** |
||
| 1525 | * Utility function to calculate the variance with or without |
||
| 1526 | * a fixed mean |
||
| 1527 | * |
||
| 1528 | * @access private |
||
| 1529 | * @param $mean the fixed mean to use, null as default |
||
| 1530 | * @return mixed a numeric value on success, a PEAR_Error otherwise |
||
| 1531 | * @see variance() |
||
| 1532 | * @see varianceWithMean() |
||
| 1533 | */ |
||
| 1534 | public function __calcVariance($mean = null) |
||
| 1535 | { |
||
| 1536 | if ($this->_data == null) { |
||
| 1537 | throw new \PEAR_Exception('data has not been set'); |
||
| 1538 | } |
||
| 1539 | try { |
||
| 1540 | $sumdiff2 = $this->__sumdiff(2, $mean); |
||
| 1541 | try { |
||
| 1542 | $count = $this->count(); |
||
| 1543 | } catch (\PEAR_Exception $e) { |
||
| 1544 | return $count; |
||
| 1545 | } |
||
| 1546 | } catch (\PEAR_Exception $e) { |
||
| 1547 | return $sumdiff2; |
||
| 1548 | } |
||
| 1549 | |||
| 1550 | if ($count == 1) { |
||
| 1551 | throw new \PEAR_Exception('cannot calculate variance of a singe data point'); |
||
| 1552 | } |
||
| 1553 | return ($sumdiff2 / ($count - 1)); |
||
| 1554 | } |
||
| 1555 | |||
| 1556 | /** |
||
| 1557 | * Utility function to calculate the absolute deviation with or without |
||
| 1558 | * a fixed mean |
||
| 1559 | * |
||
| 1560 | * @access private |
||
| 1561 | * @param $mean the fixed mean to use, null as default |
||
| 1562 | * @return mixed a numeric value on success, a PEAR_Error otherwise |
||
| 1563 | * @see absDev() |
||
| 1564 | * @see absDevWithMean() |
||
| 1565 | */ |
||
| 1566 | public function __calcAbsoluteDeviation($mean = null) |
||
| 1567 | { |
||
| 1568 | if ($this->_data == null) { |
||
| 1569 | throw new \PEAR_Exception('data has not been set'); |
||
| 1570 | } |
||
| 1571 | try { |
||
| 1572 | $count = $this->count(); |
||
| 1573 | try { |
||
| 1574 | $sumabsdev = $this->__sumabsdev($mean); |
||
| 1575 | } catch (\PEAR_Exception $e) { |
||
| 1576 | return $sumabsdev; |
||
| 1577 | } |
||
| 1578 | } catch (\PEAR_Exception $e) { |
||
| 1579 | return $count; |
||
| 1580 | } |
||
| 1581 | |||
| 1582 | return $sumabsdev / $count; |
||
| 1583 | } |
||
| 1584 | |||
| 1585 | /** |
||
| 1586 | * Utility function to calculate: SUM { | xi - mean | } |
||
| 1587 | * |
||
| 1588 | * @access private |
||
| 1589 | * @param optional double $mean the mean value for the set or population |
||
| 1590 | * @return mixed the sum on success, a PEAR_Error object otherwise |
||
| 1591 | * |
||
| 1592 | * @see absDev() |
||
| 1593 | * @see absDevWithMean() |
||
| 1594 | */ |
||
| 1595 | public function __sumabsdev($mean = null) |
||
| 1596 | { |
||
| 1597 | if ($this->_data == null) { |
||
| 1598 | throw new \PEAR_Exception('data has not been set'); |
||
| 1599 | } |
||
| 1600 | if (is_null($mean)) { |
||
| 1601 | $mean = $this->mean(); |
||
| 1602 | } |
||
| 1603 | $sdev = 0; |
||
| 1604 | if ($this->_dataOption == self::STATS_DATA_CUMMULATIVE) { |
||
| 1605 | foreach ($this->_data as $val => $freq) { |
||
| 1606 | $sdev += $freq * abs($val - $mean); |
||
| 1607 | } |
||
| 1608 | } else { |
||
| 1609 | foreach ($this->_data as $val) { |
||
| 1610 | $sdev += abs($val - $mean); |
||
| 1611 | } |
||
| 1612 | } |
||
| 1613 | return $sdev; |
||
| 1614 | } |
||
| 1615 | |||
| 1616 | /** |
||
| 1617 | * Utility function to format a PEAR_Error to be used by calc(), |
||
| 1618 | * calcBasic() and calcFull() |
||
| 1619 | * |
||
| 1620 | * @access private |
||
| 1621 | * @param mixed $v value to be formatted |
||
| 1622 | * @param boolean $returnErrorObject whether the raw PEAR_Error (when true, default), |
||
| 1623 | * or only the error message will be returned (when false) |
||
| 1624 | * @return mixed if the value is a PEAR_Error object, and $useErrorObject |
||
| 1625 | * is false, then a string with the error message will be returned, |
||
| 1626 | * otherwise the value will not be modified and returned as passed. |
||
| 1627 | */ |
||
| 1628 | public function __format($v, $useErrorObject = true) |
||
| 1634 | } |
||
| 1635 | } |
||
| 1636 | |||
| 1637 | /** |
||
| 1638 | * Utility function to validate the data and modify it |
||
| 1639 | * according to the current null handling option |
||
| 1640 | * |
||
| 1641 | * @access private |
||
| 1642 | * @return mixed true on success, a PEAR_Error object otherwise |
||
| 1643 | * |
||
| 1644 | * @see setData() |
||
| 1645 | */ |
||
| 1646 | public function _validate() |
||
| 1647 | { |
||
| 1648 | $cummulativeData = ($this->_dataOption == self::STATS_DATA_CUMMULATIVE); |
||
| 1649 | foreach ($this->_data as $key => $value) { |
||
| 1650 | $d = ($cummulativeData) ? $key : $value; |
||
| 1651 | $v = ($cummulativeData) ? $value : $key; |
||
| 1652 | if (!is_numeric($d)) { |
||
| 1653 | switch ($this->_nullOption) { |
||
| 1654 | case self::STATS_IGNORE_NULL: |
||
| 1655 | unset($this->_data["$key"]); |
||
| 1656 | break; |
||
| 1657 | case self::STATS_USE_NULL_AS_ZERO: |
||
| 1658 | if ($cummulativeData) { |
||
| 1659 | unset($this->_data["$key"]); |
||
| 1660 | // TODO: shift up? |
||
| 1661 | if (!isset($this->_data[0])) { |
||
| 1662 | $this->_data[0] = 0; |
||
| 1663 | } |
||
| 1664 | $this->_data[0] += $v; |
||
| 1665 | } else { |
||
| 1666 | $this->_data[$key] = 0; |
||
| 1667 | } |
||
| 1668 | break; |
||
| 1669 | case self::STATS_REJECT_NULL: |
||
| 1670 | default: |
||
| 1671 | throw new \PEAR_Exception('data rejected, contains NULL values'); |
||
| 1672 | break; |
||
| 1710 | } |
||
| 1711 | } |
||
| 1712 | |||
| 1715 |
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