<?php
//
// +----------------------------------------------------------------------+
// | PHP Version 4 |
// +----------------------------------------------------------------------+
// | Copyright (c) 1997-2003 The PHP Group |
// +----------------------------------------------------------------------+
// | This source file is subject to version 2.0 of the PHP license, |
// | that is bundled with this package in the file LICENSE, and is |
// | available at through the world-wide-web at |
// | http://www.php.net/license/2_02.txt. |
// | If you did not receive a copy of the PHP license and are unable to |
// | obtain it through the world-wide-web, please send a note to |
// | license@php.net so we can mail you a copy immediately. |
// +----------------------------------------------------------------------+
// | Authors: Jesus M. Castagnetto <jmcastagnetto@php.net> |
// +----------------------------------------------------------------------+
//
// $Id: Stats.php,v 1.15 2003/06/01 11:40:30 jmcastagnetto Exp $
//
include_once 'PEAR.php';
/**
* @package Math_Stats
*/
// Constants for defining the statistics to calculate /*{{{*/
/**
* STATS_BASIC to generate the basic descriptive statistics
*/
define('STATS_BASIC', 1);
/**
* STATS_FULL to generate also higher moments, mode, median, etc.
*/
define('STATS_FULL', 2);
/*}}}*/
// Constants describing the data set format /*{{{*/
/**
* STATS_DATA_SIMPLE for an array of numeric values. This is the default.
* e.g. $data = array(2,3,4,5,1,1,6);
*/
define('STATS_DATA_SIMPLE', 0);
/**
* STATS_DATA_CUMMULATIVE for an associative array of frequency values,
* where in each array entry, the index is the data point and the
* value the count (frequency):
* e.g. $data = array(3=>4, 2.3=>5, 1.25=>6, 0.5=>3)
*/
define('STATS_DATA_CUMMULATIVE', 1);
/*}}}*/
// Constants defining how to handle nulls /*{{{*/
/**
* STATS_REJECT_NULL, reject data sets with null values. This is the default.
* Any non-numeric value is considered a null in this context.
*/
define('STATS_REJECT_NULL', -1);
/**
* STATS_IGNORE_NULL, ignore null values and prune them from the data.
* Any non-numeric value is considered a null in this context.
*/
define('STATS_IGNORE_NULL', -2);
/**
* STATS_USE_NULL_AS_ZERO, assign the value of 0 (zero) to null values.
* Any non-numeric value is considered a null in this context.
*/
define('STATS_USE_NULL_AS_ZERO', -3);
/*}}}*/
/**
* A class to calculate descriptive statistics from a data set.
* Data sets can be simple arrays of data, or a cummulative hash.
* The second form is useful when passing large data set,
* for example the data set:
*
* <pre>
* $data1 = array (1,2,1,1,1,1,3,3,4.1,3,2,2,4.1,1,1,2,3,3,2,2,1,1,2,2);
* </pre>
*
* can be epxressed more compactly as:
*
* <pre>
* $data2 = array('1'=>9, '2'=>8, '3'=>5, '4.1'=>2);
* </pre>
*
* Example of use:
*
* <pre>
* include_once 'Math/Stats.php';
* $s = new Math_Stats();
* $s->setData($data1);
* // or
* // $s->setData($data2, STATS_DATA_CUMMULATIVE);
* $stats = $s->calcBasic();
* echo 'Mean: '.$stats['mean'].' StDev: '.$stats['stdev'].' <br />\n';
*
* // using data with nulls
* // first ignoring them:
* $data3 = array(1.2, 'foo', 2.4, 3.1, 4.2, 3.2, null, 5.1, 6.2);
* $s->setNullOption(STATS_IGNORE_NULL);
* $s->setData($data3);
* $stats3 = $s->calcFull();
*
* // and then assuming nulls == 0
* $s->setNullOption(STATS_USE_NULL_AS_ZERO);
* $s->setData($data3);
* $stats3 = $s->calcFull();
* </pre>
*
* Originally this class was part of NumPHP (Numeric PHP package)
*
* @author Jesus M. Castagnetto <jmcastagnetto@php.net>
* @version 0.8
* @access public
* @package Math_Stats
*/
class Base {/*{{{*/
// properties /*{{{*/
/**
* The simple or cummulative data set.
* Null by default.
*
* @access private
* @var array
*/
public $_data = null;
/**
* Expanded data set. Only set when cummulative data
* is being used. Null by default.
*
* @access private
* @var array
*/
public $_dataExpanded = null;
/**
* Flag for data type, one of STATS_DATA_SIMPLE or
* STATS_DATA_CUMMULATIVE. Null by default.
*
* @access private
* @var int
*/
public $_dataOption = null;
/**
* Flag for null handling options. One of STATS_REJECT_NULL,
* STATS_IGNORE_NULL or STATS_USE_NULL_AS_ZERO
*
* @access private
* @var int
*/
public $_nullOption;
/**
* Array for caching result values, should be reset
* when using setData()
*
* @access private
* @var array
*/
public $_calculatedValues = array();
/*}}}*/
/**
* Constructor for the class
*
* @access public
* @param optional int $nullOption how to handle null values
* @return object Math_Stats
*/
function Math_Stats($nullOption=STATS_REJECT_NULL) {/*{{{*/
$this->_nullOption = $nullOption;
}/*}}}*/
/**
* Sets and verifies the data, checking for nulls and using
* the current null handling option
*
* @access public
* @param array $arr the data set
* @param optional int $opt data format: STATS_DATA_CUMMULATIVE or STATS_DATA_SIMPLE (default)
* @return mixed true on success, a PEAR_Error object otherwise
*/
function setData($arr, $opt=STATS_DATA_SIMPLE) {/*{{{*/
if (!is_array($arr)) {
return PEAR::raiseError('invalid data, an array of numeric data was expected');
}
$this->_data = null;
$this->_dataExpanded = null;
$this->_dataOption = null;
$this->_calculatedValues = array();
if ($opt == STATS_DATA_SIMPLE) {
$this->_dataOption = $opt;
$this->_data = array_values($arr);
} else if ($opt == STATS_DATA_CUMMULATIVE) {
$this->_dataOption = $opt;
$this->_data = $arr;
$this->_dataExpanded = array();
}
return $this->_validate();
}/*}}}*/
/**
* Returns the data which might have been modified
* according to the current null handling options.
*
* @access public
* @param boolean $expanded whether to return a expanded list, default is false
* @return mixed array of data on success, a PEAR_Error object otherwise
* @see _validate()
*/
function getData($expanded=false) {/*{{{*/
if ($this->_data == null) {
return PEAR::raiseError('data has not been set');
}
if ($this->_dataOption == STATS_DATA_CUMMULATIVE && $expanded) {
return $this->_dataExpanded;
} else {
return $this->_data;
}
}/*}}}*/
/**
* Sets the null handling option.
* Must be called before assigning a new data set containing null values
*
* @access public
* @return mixed true on success, a PEAR_Error object otherwise
* @see _validate()
*/
function setNullOption($nullOption) {/*{{{*/
if ($nullOption == STATS_REJECT_NULL
|| $nullOption == STATS_IGNORE_NULL
|| $nullOption == STATS_USE_NULL_AS_ZERO) {
$this->_nullOption = $nullOption;
return true;
} else {
return PEAR::raiseError('invalid null handling option expecting: '.
'STATS_REJECT_NULL, STATS_IGNORE_NULL or STATS_USE_NULL_AS_ZERO');
}
}/*}}}*/
/**
* Transforms the data by substracting each entry from the mean and
* dividing by its standard deviation. This will reset all pre-calculated
* values to their original (unset) defaults.
*
* @access public
* @return mixed true on success, a PEAR_Error object otherwise
* @see mean()
* @see stDev()
* @see setData()
*/
function studentize() {/*{{{*/
$mean = $this->mean();
if (PEAR::isError($mean)) {
return $mean;
}
$std = $this->stDev();
if (PEAR::isError($std)) {
return $std;
}
if ($std == 0) {
return PEAR::raiseError('cannot studentize data, standard deviation is zero.');
}
$arr = array();
if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
foreach ($this->_data as $val=>$freq) {
$newval = ($val - $mean) / $std;
$arr["$newval"] = $freq;
}
} else {
foreach ($this->_data as $val) {
$newval = ($val - $mean) / $std;
$arr[] = $newval;
}
}
return $this->setData($arr, $this->_dataOption);
}/*}}}*/
/**
* Transforms the data by substracting each entry from the mean.
* This will reset all pre-calculated values to their original (unset) defaults.
*
* @access public
* @return mixed true on success, a PEAR_Error object otherwise
* @see mean()
* @see setData()
*/
function center() {/*{{{*/
$mean = $this->mean();
if (PEAR::isError($mean)) {
return $mean;
}
$arr = array();
if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
foreach ($this->_data as $val=>$freq) {
$newval = $val - $mean;
$arr["$newval"] = $freq;
}
} else {
foreach ($this->_data as $val) {
$newval = $val - $mean;
$arr[] = $newval;
}
}
return $this->setData($arr, $this->_dataOption);
}/*}}}*/
/**
* Calculates the basic or full statistics for the data set
*
* @access public
* @param int $mode one of STATS_BASIC or STATS_FULL
* @param boolean $returnErrorObject whether the raw PEAR_Error (when true, default),
* or only the error message will be returned (when false), if an error happens.
* @return mixed an associative array of statistics on success, a PEAR_Error object otherwise
* @see calcBasic()
* @see calcFull()
*/
function calc($mode, $returnErrorObject=true) {/*{{{*/
if ($this->_data == null) {
return PEAR::raiseError('data has not been set');
}
if ($mode == STATS_BASIC) {
return $this->calcBasic($returnErrorObject);
} elseif ($mode == STATS_FULL) {
return $this->calcFull($returnErrorObject);
} else {
return PEAR::raiseError('incorrect mode, expected STATS_BASIC or STATS_FULL');
}
}/*}}}*/
/**
* Calculates a basic set of statistics
*
* @access public
* @param boolean $returnErrorObject whether the raw PEAR_Error (when true, default),
* or only the error message will be returned (when false), if an error happens.
* @return mixed an associative array of statistics on success, a PEAR_Error object otherwise
* @see calc()
* @see calcFull()
*/
function calcBasic($returnErrorObject=true) {/*{{{*/
return array (
'min' => $this->__format($this->min(), $returnErrorObject),
'max' => $this->__format($this->max(), $returnErrorObject),
'sum' => $this->__format($this->sum(), $returnErrorObject),
'sum2' => $this->__format($this->sum2(), $returnErrorObject),
'count' => $this->__format($this->count(), $returnErrorObject),
'mean' => $this->__format($this->mean(), $returnErrorObject),
'stdev' => $this->__format($this->stDev(), $returnErrorObject),
'variance' => $this->__format($this->variance(), $returnErrorObject),
'range' => $this->__format($this->range(), $returnErrorObject)
);
}/*}}}*/
/**
* Calculates a full set of statistics
*
* @access public
* @param boolean $returnErrorObject whether the raw PEAR_Error (when true, default),
* or only the error message will be returned (when false), if an error happens.
* @return mixed an associative array of statistics on success, a PEAR_Error object otherwise
* @see calc()
* @see calcBasic()
*/
function calcFull($returnErrorObject=true) {/*{{{*/
return array (
'min' => $this->__format($this->min(), $returnErrorObject),
'max' => $this->__format($this->max(), $returnErrorObject),
'sum' => $this->__format($this->sum(), $returnErrorObject),
'sum2' => $this->__format($this->sum2(), $returnErrorObject),
'count' => $this->__format($this->count(), $returnErrorObject),
'mean' => $this->__format($this->mean(), $returnErrorObject),
'median' => $this->__format($this->median(), $returnErrorObject),
'mode' => $this->__format($this->mode(), $returnErrorObject),
'midrange' => $this->__format($this->midrange(), $returnErrorObject),
'geometric_mean' => $this->__format($this->geometricMean(), $returnErrorObject),
'harmonic_mean' => $this->__format($this->harmonicMean(), $returnErrorObject),
'stdev' => $this->__format($this->stDev(), $returnErrorObject),
'absdev' => $this->__format($this->absDev(), $returnErrorObject),
'variance' => $this->__format($this->variance(), $returnErrorObject),
'range' => $this->__format($this->range(), $returnErrorObject),
'std_error_of_mean' => $this->__format($this->stdErrorOfMean(), $returnErrorObject),
'skewness' => $this->__format($this->skewness(), $returnErrorObject),
'kurtosis' => $this->__format($this->kurtosis(), $returnErrorObject),
'coeff_of_variation' => $this->__format($this->coeffOfVariation(), $returnErrorObject),
'sample_central_moments' => array (
1 => $this->__format($this->sampleCentralMoment(1), $returnErrorObject),
2 => $this->__format($this->sampleCentralMoment(2), $returnErrorObject),
3 => $this->__format($this->sampleCentralMoment(3), $returnErrorObject),
4 => $this->__format($this->sampleCentralMoment(4), $returnErrorObject),
5 => $this->__format($this->sampleCentralMoment(5), $returnErrorObject)
),
'sample_raw_moments' => array (
1 => $this->__format($this->sampleRawMoment(1), $returnErrorObject),
2 => $this->__format($this->sampleRawMoment(2), $returnErrorObject),
3 => $this->__format($this->sampleRawMoment(3), $returnErrorObject),
4 => $this->__format($this->sampleRawMoment(4), $returnErrorObject),
5 => $this->__format($this->sampleRawMoment(5), $returnErrorObject)
),
'frequency' => $this->__format($this->frequency(), $returnErrorObject),
'quartiles' => $this->__format($this->quartiles(), $returnErrorObject),
'interquartile_range' => $this->__format($this->interquartileRange(), $returnErrorObject),
'interquartile_mean' => $this->__format($this->interquartileMean(), $returnErrorObject),
'quartile_deviation' => $this->__format($this->quartileDeviation(), $returnErrorObject),
'quartile_variation_coefficient' => $this->__format($this->quartileVariationCoefficient(), $returnErrorObject),
'quartile_skewness_coefficient' => $this->__format($this->quartileSkewnessCoefficient(), $returnErrorObject)
);
}/*}}}*/
/**
* Calculates the minimum of a data set.
* Handles cummulative data sets correctly
*
* @access public
* @return mixed the minimum value on success, a PEAR_Error object otherwise
* @see calc()
* @see max()
*/
function min() {/*{{{*/
if ($this->_data == null) {
return PEAR::raiseError('data has not been set');
}
if (!array_key_exists('min', $this->_calculatedValues)) {
if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
$min = min(array_keys($this->_data));
} else {
$min = min($this->_data);
}
$this->_calculatedValues['min'] = $min;
}
return $this->_calculatedValues['min'];
}/*}}}*/
/**
* Calculates the maximum of a data set.
* Handles cummulative data sets correctly
*
* @access public
* @return mixed the maximum value on success, a PEAR_Error object otherwise
* @see calc()
* @see min()
*/
function max() {/*{{{*/
if ($this->_data == null) {
return PEAR::raiseError('data has not been set');
}
if (!array_key_exists('max', $this->_calculatedValues)) {
if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
$max = max(array_keys($this->_data));
} else {
$max = max($this->_data);
}
$this->_calculatedValues['max'] = $max;
}
return $this->_calculatedValues['max'];
}/*}}}*/
/**
* Calculates SUM { xi }
* Handles cummulative data sets correctly
*
* @access public
* @return mixed the sum on success, a PEAR_Error object otherwise
* @see calc()
* @see sum2()
* @see sumN()
*/
function sum() {/*{{{*/
if (!array_key_exists('sum', $this->_calculatedValues)) {
$sum = $this->sumN(1);
if (PEAR::isError($sum)) {
return $sum;
} else {
$this->_calculatedValues['sum'] = $sum;
}
}
return $this->_calculatedValues['sum'];
}/*}}}*/
/**
* Calculates SUM { (xi)^2 }
* Handles cummulative data sets correctly
*
* @access public
* @return mixed the sum on success, a PEAR_Error object otherwise
* @see calc()
* @see sum()
* @see sumN()
*/
function sum2() {/*{{{*/
if (!array_key_exists('sum2', $this->_calculatedValues)) {
$sum2 = $this->sumN(2);
if (PEAR::isError($sum2)) {
return $sum2;
} else {
$this->_calculatedValues['sum2'] = $sum2;
}
}
return $this->_calculatedValues['sum2'];
}/*}}}*/
/**
* Calculates SUM { (xi)^n }
* Handles cummulative data sets correctly
*
* @access public
* @param numeric $n the exponent
* @return mixed the sum on success, a PEAR_Error object otherwise
* @see calc()
* @see sum()
* @see sum2()
*/
function sumN($n) {/*{{{*/
if ($this->_data == null) {
return PEAR::raiseError('data has not been set');
}
$sumN = 0;
if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
foreach($this->_data as $val=>$freq) {
$sumN += $freq * pow((double)$val, (double)$n);
}
} else {
foreach($this->_data as $val) {
$sumN += pow((double)$val, (double)$n);
}
}
return $sumN;
}/*}}}*/
/**
* Calculates PROD { (xi) }, (the product of all observations)
* Handles cummulative data sets correctly
*
* @access public
* @return mixed the product on success, a PEAR_Error object otherwise
* @see productN()
*/
function product() {/*{{{*/
if (!array_key_exists('product', $this->_calculatedValues)) {
$product = $this->productN(1);
if (PEAR::isError($product)) {
return $product;
} else {
$this->_calculatedValues['product'] = $product;
}
}
return $this->_calculatedValues['product'];
}/*}}}*/
/**
* Calculates PROD { (xi)^n }, which is the product of all observations
* Handles cummulative data sets correctly
*
* @access public
* @param numeric $n the exponent
* @return mixed the product on success, a PEAR_Error object otherwise
* @see product()
*/
function productN($n) {/*{{{*/
if ($this->_data == null) {
return PEAR::raiseError('data has not been set');
}
$prodN = 1.0;
if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
foreach($this->_data as $val=>$freq) {
if ($val == 0) {
return 0.0;
}
$prodN *= $freq * pow((double)$val, (double)$n);
}
} else {
foreach($this->_data as $val) {
if ($val == 0) {
return 0.0;
}
$prodN *= pow((double)$val, (double)$n);
}
}
return $prodN;
}/*}}}*/
/**
* Calculates the number of data points in the set
* Handles cummulative data sets correctly
*
* @access public
* @return mixed the count on success, a PEAR_Error object otherwise
* @see calc()
*/
function count() {/*{{{*/
if ($this->_data == null) {
return PEAR::raiseError('data has not been set');
}
if (!array_key_exists('count', $this->_calculatedValues)) {
if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
$count = count($this->_dataExpanded);
} else {
$count = count($this->_data);
}
$this->_calculatedValues['count'] = $count;
}
return $this->_calculatedValues['count'];
}/*}}}*/
/**
* Calculates the mean (average) of the data points in the set
* Handles cummulative data sets correctly
*
* @access public
* @return mixed the mean value on success, a PEAR_Error object otherwise
* @see calc()
* @see sum()
* @see count()
*/
function mean() {/*{{{*/
if (!array_key_exists('mean', $this->_calculatedValues)) {
$sum = $this->sum();
if (PEAR::isError($sum)) {
return $sum;
}
$count = $this->count();
if (PEAR::isError($count)) {
return $count;
}
$this->_calculatedValues['mean'] = $sum / $count;
}
return $this->_calculatedValues['mean'];
}/*}}}*/
/**
* Calculates the range of the data set = max - min
*
* @access public
* @return mixed the value of the range on success, a PEAR_Error object otherwise.
*/
function range() {/*{{{*/
if (!array_key_exists('range', $this->_calculatedValues)) {
$min = $this->min();
if (PEAR::isError($min)) {
return $min;
}
$max = $this->max();
if (PEAR::isError($max)) {
return $max;
}
$this->_calculatedValues['range'] = $max - $min;
}
return $this->_calculatedValues['range'];
}/*}}}*/
/**
* Calculates the variance (unbiased) of the data points in the set
* Handles cummulative data sets correctly
*
* @access public
* @return mixed the variance value on success, a PEAR_Error object otherwise
* @see calc()
* @see __sumdiff()
* @see count()
*/
function variance() {/*{{{*/
if (!array_key_exists('variance', $this->_calculatedValues)) {
$variance = $this->__calcVariance();
if (PEAR::isError($variance)) {
return $variance;
}
$this->_calculatedValues['variance'] = $variance;
}
return $this->_calculatedValues['variance'];
}/*}}}*/
/**
* Calculates the standard deviation (unbiased) of the data points in the set
* Handles cummulative data sets correctly
*
* @access public
* @return mixed the standard deviation on success, a PEAR_Error object otherwise
* @see calc()
* @see variance()
*/
function stDev() {/*{{{*/
if (!array_key_exists('stDev', $this->_calculatedValues)) {
$variance = $this->variance();
if (PEAR::isError($variance)) {
return $variance;
}
$this->_calculatedValues['stDev'] = sqrt($variance);
}
return $this->_calculatedValues['stDev'];
}/*}}}*/
/**
* Calculates the variance (unbiased) of the data points in the set
* given a fixed mean (average) value. Not used in calcBasic(), calcFull()
* or calc().
* Handles cummulative data sets correctly
*
* @access public
* @param numeric $mean the fixed mean value
* @return mixed the variance on success, a PEAR_Error object otherwise
* @see __sumdiff()
* @see count()
* @see variance()
*/
function varianceWithMean($mean) {/*{{{*/
return $this->__calcVariance($mean);
}/*}}}*/
/**
* Calculates the standard deviation (unbiased) of the data points in the set
* given a fixed mean (average) value. Not used in calcBasic(), calcFull()
* or calc().
* Handles cummulative data sets correctly
*
* @access public
* @param numeric $mean the fixed mean value
* @return mixed the standard deviation on success, a PEAR_Error object otherwise
* @see varianceWithMean()
* @see stDev()
*/
function stDevWithMean($mean) {/*{{{*/
$varianceWM = $this->varianceWithMean($mean);
if (PEAR::isError($varianceWM)) {
return $varianceWM;
}
return sqrt($varianceWM);
}/*}}}*/
/**
* Calculates the absolute deviation of the data points in the set
* Handles cummulative data sets correctly
*
* @access public
* @return mixed the absolute deviation on success, a PEAR_Error object otherwise
* @see calc()
* @see __sumabsdev()
* @see count()
* @see absDevWithMean()
*/
function absDev() {/*{{{*/
if (!array_key_exists('absDev', $this->_calculatedValues)) {
$absDev = $this->__calcAbsoluteDeviation();
if (PEAR::isError($absdev)) {
return $absdev;
}
$this->_calculatedValues['absDev'] = $absDev;
}
return $this->_calculatedValues['absDev'];
}/*}}}*/
/**
* Calculates the absolute deviation of the data points in the set
* given a fixed mean (average) value. Not used in calcBasic(), calcFull()
* or calc().
* Handles cummulative data sets correctly
*
* @access public
* @param numeric $mean the fixed mean value
* @return mixed the absolute deviation on success, a PEAR_Error object otherwise
* @see __sumabsdev()
* @see absDev()
*/
function absDevWithMean($mean) {/*{{{*/
return $this->__calcAbsoluteDeviation($mean);
}/*}}}*/
/**
* Calculates the skewness of the data distribution in the set
* The skewness measures the degree of asymmetry of a distribution,
* and is related to the third central moment of a distribution.
* A normal distribution has a skewness = 0
* A distribution with a tail off towards the high end of the scale
* (positive skew) has a skewness > 0
* A distribution with a tail off towards the low end of the scale
* (negative skew) has a skewness < 0
* Handles cummulative data sets correctly
*
* @access public
* @return mixed the skewness value on success, a PEAR_Error object otherwise
* @see __sumdiff()
* @see count()
* @see stDev()
* @see calc()
*/
function skewness() {/*{{{*/
if (!array_key_exists('skewness', $this->_calculatedValues)) {
$count = $this->count();
if (PEAR::isError($count)) {
return $count;
}
$stDev = $this->stDev();
if (PEAR::isError($stDev)) {
return $stDev;
}
$sumdiff3 = $this->__sumdiff(3);
if (PEAR::isError($sumdiff3)) {
return $sumdiff3;
}
$this->_calculatedValues['skewness'] = ($sumdiff3 / ($count * pow($stDev, 3)));
}
return $this->_calculatedValues['skewness'];
}/*}}}*/
/**
* Calculates the kurtosis of the data distribution in the set
* The kurtosis measures the degrees of peakedness of a distribution.
* It is also called the "excess" or "excess coefficient", and is
* a normalized form of the fourth central moment of a distribution.
* A normal distributions has kurtosis = 0
* A narrow and peaked (leptokurtic) distribution has a
* kurtosis > 0
* A flat and wide (platykurtic) distribution has a kurtosis < 0
* Handles cummulative data sets correctly
*
* @access public
* @return mixed the kurtosis value on success, a PEAR_Error object otherwise
* @see __sumdiff()
* @see count()
* @see stDev()
* @see calc()
*/
function kurtosis() {/*{{{*/
if (!array_key_exists('kurtosis', $this->_calculatedValues)) {
$count = $this->count();
if (PEAR::isError($count)) {
return $count;
}
$stDev = $this->stDev();
if (PEAR::isError($stDev)) {
return $stDev;
}
$sumdiff4 = $this->__sumdiff(4);
if (PEAR::isError($sumdiff4)) {
return $sumdiff4;
}
$this->_calculatedValues['kurtosis'] = ($sumdiff4 / ($count * pow($stDev, 4))) - 3;
}
return $this->_calculatedValues['kurtosis'];
}/*}}}*/
/**
* Calculates the median of a data set.
* The median is the value such that half of the points are below it
* in a sorted data set.
* If the number of values is odd, it is the middle item.
* If the number of values is even, is the average of the two middle items.
* Handles cummulative data sets correctly
*
* @access public
* @return mixed the median value on success, a PEAR_Error object otherwise
* @see count()
* @see calc()
*/
function median() {/*{{{*/
if ($this->_data == null) {
return PEAR::raiseError('data has not been set');
}
if (!array_key_exists('median', $this->_calculatedValues)) {
if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
$arr =& $this->_dataExpanded;
} else {
$arr =& $this->_data;
}
$n = $this->count();
if (PEAR::isError($n)) {
return $n;
}
$h = intval($n / 2);
if ($n % 2 == 0) {
$median = ($arr[$h] + $arr[$h - 1]) / 2;
} else {
$median = $arr[$h + 1];
}
$this->_calculatedValues['median'] = $median;
}
return $this->_calculatedValues['median'];
}/*}}}*/
/**
* Calculates the mode of a data set.
* The mode is the value with the highest frequency in the data set.
* There can be more than one mode.
* Handles cummulative data sets correctly
*
* @access public
* @return mixed an array of mode value on success, a PEAR_Error object otherwise
* @see frequency()
* @see calc()
*/
function mode() {/*{{{*/
if ($this->_data == null) {
return PEAR::raiseError('data has not been set');
}
if (!array_key_exists('mode', $this->_calculatedValues)) {
if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
$arr = $this->_data;
} else {
$arr = $this->frequency();
}
arsort($arr);
$mcount = 1;
foreach ($arr as $val=>$freq) {
if ($mcount == 1) {
$mode = array($val);
$mfreq = $freq;
++$mcount;
continue;
}
if ($mfreq == $freq)
$mode[] = $val;
if ($mfreq > $freq)
break;
}
$this->_calculatedValues['mode'] = $mode;
}
return $this->_calculatedValues['mode'];
}/*}}}*/
/**
* Calculates the midrange of a data set.
* The midrange is the average of the minimum and maximum of the data set.
* Handles cummulative data sets correctly
*
* @access public
* @return mixed the midrange value on success, a PEAR_Error object otherwise
* @see min()
* @see max()
* @see calc()
*/
function midrange() {/*{{{*/
if (!array_key_exists('midrange', $this->_calculatedValues)) {
$min = $this->min();
if (PEAR::isError($min)) {
return $min;
}
$max = $this->max();
if (PEAR::isError($max)) {
return $max;
}
$this->_calculatedValues['midrange'] = (($max + $min) / 2);
}
return $this->_calculatedValues['midrange'];
}/*}}}*/
/**
* Calculates the geometrical mean of the data points in the set
* Handles cummulative data sets correctly
*
* @access public
* @return mixed the geometrical mean value on success, a PEAR_Error object otherwise
* @see calc()
* @see product()
* @see count()
*/
function geometricMean() {/*{{{*/
if (!array_key_exists('geometricMean', $this->_calculatedValues)) {
$count = $this->count();
if (PEAR::isError($count)) {
return $count;
}
$prod = $this->product();
if (PEAR::isError($prod)) {
return $prod;
}
if ($prod == 0.0) {
return 0.0;
}
if ($prod < 0) {
return PEAR::raiseError('The product of the data set is negative, geometric mean undefined.');
}
$this->_calculatedValues['geometricMean'] = pow($prod , 1 / $count);
}
return $this->_calculatedValues['geometricMean'];
}/*}}}*/
/**
* Calculates the harmonic mean of the data points in the set
* Handles cummulative data sets correctly
*
* @access public
* @return mixed the harmonic mean value on success, a PEAR_Error object otherwise
* @see calc()
* @see count()
*/
function harmonicMean() {/*{{{*/
if ($this->_data == null) {
return PEAR::raiseError('data has not been set');
}
if (!array_key_exists('harmonicMean', $this->_calculatedValues)) {
$count = $this->count();
if (PEAR::isError($count)) {
return $count;
}
$invsum = 0.0;
if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
foreach($this->_data as $val=>$freq) {
if ($val == 0) {
return PEAR::raiseError('cannot calculate a '.
'harmonic mean with data values of zero.');
}
$invsum += $freq / $val;
}
} else {
foreach($this->_data as $val) {
if ($val == 0) {
return PEAR::raiseError('cannot calculate a '.
'harmonic mean with data values of zero.');
}
$invsum += 1 / $val;
}
}
$this->_calculatedValues['harmonicMean'] = $count / $invsum;
}
return $this->_calculatedValues['harmonicMean'];
}/*}}}*/
/**
* Calculates the nth central moment (m{n}) of a data set.
*
* The definition of a sample central moment is:
*
* m{n} = 1/N * SUM { (xi - avg)^n }
*
* where: N = sample size, avg = sample mean.
*
* @access public
* @param integer $n moment to calculate
* @return mixed the numeric value of the moment on success, PEAR_Error otherwise
*/
function sampleCentralMoment($n) {/*{{{*/
if (!is_int($n) || $n < 1) {
return PEAR::isError('moment must be a positive integer >= 1.');
}
if ($n == 1) {
return 0;
}
$count = $this->count();
if (PEAR::isError($count)) {
return $count;
}
if ($count == 0) {
return PEAR::raiseError("Cannot calculate {$n}th sample moment, ".
'there are zero data entries');
}
$sum = $this->__sumdiff($n);
if (PEAR::isError($sum)) {
return $sum;
}
return ($sum / $count);
}/*}}}*/
/**
* Calculates the nth raw moment (m{n}) of a data set.
*
* The definition of a sample central moment is:
*
* m{n} = 1/N * SUM { xi^n }
*
* where: N = sample size, avg = sample mean.
*
* @access public
* @param integer $n moment to calculate
* @return mixed the numeric value of the moment on success, PEAR_Error otherwise
*/
function sampleRawMoment($n) {/*{{{*/
if (!is_int($n) || $n < 1) {
return PEAR::isError('moment must be a positive integer >= 1.');
}
$count = $this->count();
if (PEAR::isError($count)) {
return $count;
}
if ($count == 0) {
return PEAR::raiseError("Cannot calculate {$n}th raw moment, ".
'there are zero data entries.');
}
$sum = $this->sumN($n);
if (PEAR::isError($sum)) {
return $sum;
}
return ($sum / $count);
}/*}}}*/
/**
* Calculates the coefficient of variation of a data set.
* The coefficient of variation measures the spread of a set of data
* as a proportion of its mean. It is often expressed as a percentage.
* Handles cummulative data sets correctly
*
* @access public
* @return mixed the coefficient of variation on success, a PEAR_Error object otherwise
* @see stDev()
* @see mean()
* @see calc()
*/
function coeffOfVariation() {/*{{{*/
if (!array_key_exists('coeffOfVariation', $this->_calculatedValues)) {
$mean = $this->mean();
if (PEAR::isError($mean)) {
return $mean;
}
if ($mean == 0.0) {
return PEAR::raiseError('cannot calculate the coefficient '.
'of variation, mean of sample is zero');
}
$stDev = $this->stDev();
if (PEAR::isError($stDev)) {
return $stDev;
}
$this->_calculatedValues['coeffOfVariation'] = $stDev / $mean;
}
return $this->_calculatedValues['coeffOfVariation'];
}/*}}}*/
/**
* Calculates the standard error of the mean.
* It is the standard deviation of the sampling distribution of
* the mean. The formula is:
*
* S.E. Mean = SD / (N)^(1/2)
*
* This formula does not assume a normal distribution, and shows
* that the size of the standard error of the mean is inversely
* proportional to the square root of the sample size.
*
* @access public
* @return mixed the standard error of the mean on success, a PEAR_Error object otherwise
* @see stDev()
* @see count()
* @see calc()
*/
function stdErrorOfMean() {/*{{{*/
if (!array_key_exists('stdErrorOfMean', $this->_calculatedValues)) {
$count = $this->count();
if (PEAR::isError($count)) {
return $count;
}
$stDev = $this->stDev();
if (PEAR::isError($stDev)) {
return $stDev;
}
$this->_calculatedValues['stdErrorOfMean'] = $stDev / sqrt($count);
}
return $this->_calculatedValues['stdErrorOfMean'];
}/*}}}*/
/**
* Calculates the value frequency table of a data set.
* Handles cummulative data sets correctly
*
* @access public
* @return mixed an associative array of value=>frequency items on success, a PEAR_Error object otherwise
* @see min()
* @see max()
* @see calc()
*/
function frequency() {/*{{{*/
if ($this->_data == null) {
return PEAR::raiseError('data has not been set');
}
if (!array_key_exists('frequency', $this->_calculatedValues)) {
if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
$freq = $this->_data;
} else {
$freq = array();
foreach ($this->_data as $val) {
$freq["$val"]++;
}
ksort($freq);
}
$this->_calculatedValues['frequency'] = $freq;
}
return $this->_calculatedValues['frequency'];
}/*}}}*/
/**
* The quartiles are defined as the values that divide a sorted
* data set into four equal-sized subsets, and correspond to the
* 25th, 50th, and 75th percentiles.
*
* @access public
* @return mixed an associative array of quartiles on success, a PEAR_Error otherwise
* @see percentile()
*/
function quartiles() {/*{{{*/
if (!array_key_exists('quartiles', $this->_calculatedValues)) {
$q1 = $this->percentile(25);
if (PEAR::isError($q1)) {
return $q1;
}
$q2 = $this->percentile(50);
if (PEAR::isError($q2)) {
return $q2;
}
$q3 = $this->percentile(75);
if (PEAR::isError($q3)) {
return $q3;
}
$this->_calculatedValues['quartiles'] = array (
'25' => $q1,
'50' => $q2,
'75' => $q3
);
}
return $this->_calculatedValues['quartiles'];
}/*}}}*/
/**
* The interquartile mean is defined as the mean of the values left
* after discarding the lower 25% and top 25% ranked values, i.e.:
*
* interquart mean = mean(<P(25),P(75)>)
*
* where: P = percentile
*
* @todo need to double check the equation
* @access public
* @return mixed a numeric value on success, a PEAR_Error otherwise
* @see quartiles()
*/
function interquartileMean() {/*{{{*/
if (!array_key_exists('interquartileMean', $this->_calculatedValues)) {
$quart = $this->quartiles();
if (PEAR::isError($quart)) {
return $quart;
}
$q3 = $quart['75'];
$q1 = $quart['25'];
$sum = 0;
$n = 0;
foreach ($this->getData(true) as $val) {
if ($val >= $q1 && $val <= $q3) {
$sum += $val;
++$n;
}
}
if ($n == 0) {
return PEAR::raiseError('error calculating interquartile mean, '.
'empty interquartile range of values.');
}
$this->_calculatedValues['interquartileMean'] = $sum / $n;
}
return $this->_calculatedValues['interquartileMean'];
}/*}}}*/
/**
* The interquartile range is the distance between the 75th and 25th
* percentiles. Basically the range of the middle 50% of the data set,
* and thus is not affected by outliers or extreme values.
*
* interquart range = P(75) - P(25)
*
* where: P = percentile
*
* @access public
* @return mixed a numeric value on success, a PEAR_Error otherwise
* @see quartiles()
*/
function interquartileRange() {/*{{{*/
if (!array_key_exists('interquartileRange', $this->_calculatedValues)) {
$quart = $this->quartiles();
if (PEAR::isError($quart)) {
return $quart;
}
$q3 = $quart['75'];
$q1 = $quart['25'];
$this->_calculatedValues['interquartileRange'] = $q3 - $q1;
}
return $this->_calculatedValues['interquartileRange'];
}/*}}}*/
/**
* The quartile deviation is half of the interquartile range value
*
* quart dev = (P(75) - P(25)) / 2
*
* where: P = percentile
*
* @access public
* @return mixed a numeric value on success, a PEAR_Error otherwise
* @see quartiles()
* @see interquartileRange()
*/
function quartileDeviation() {/*{{{*/
if (!array_key_exists('quartileDeviation', $this->_calculatedValues)) {
$iqr = $this->interquartileRange();
if (PEAR::isError($iqr)) {
return $iqr;
}
$this->_calculatedValues['quartileDeviation'] = $iqr / 2;
}
return $this->_calculatedValues['quartileDeviation'];
}/*}}}*/
/**
* The quartile variation coefficient is defines as follows:
*
* quart var coeff = 100 * (P(75) - P(25)) / (P(75) + P(25))
*
* where: P = percentile
*
* @todo need to double check the equation
* @access public
* @return mixed a numeric value on success, a PEAR_Error otherwise
* @see quartiles()
*/
function quartileVariationCoefficient() {/*{{{*/
if (!array_key_exists('quartileVariationCoefficient', $this->_calculatedValues)) {
$quart = $this->quartiles();
if (PEAR::isError($quart)) {
return $quart;
}
$q3 = $quart['75'];
$q1 = $quart['25'];
$d = $q3 - $q1;
$s = $q3 + $q1;
$this->_calculatedValues['quartileVariationCoefficient'] = 100 * $d / $s;
}
return $this->_calculatedValues['quartileVariationCoefficient'];
}/*}}}*/
/**
* The quartile skewness coefficient (also known as Bowley Skewness),
* is defined as follows:
*
* quart skewness coeff = (P(25) - 2*P(50) + P(75)) / (P(75) - P(25))
*
* where: P = percentile
*
* @todo need to double check the equation
* @access public
* @return mixed a numeric value on success, a PEAR_Error otherwise
* @see quartiles()
*/
function quartileSkewnessCoefficient() {/*{{{*/
if (!array_key_exists('quartileSkewnessCoefficient', $this->_calculatedValues)) {
$quart = $this->quartiles();
if (PEAR::isError($quart)) {
return $quart;
}
$q3 = $quart['75'];
$q2 = $quart['50'];
$q1 = $quart['25'];
$d = $q3 - 2*$q2 + $q1;
$s = $q3 - $q1;
$this->_calculatedValues['quartileSkewnessCoefficient'] = $d / $s;
}
return $this->_calculatedValues['quartileSkewnessCoefficient'];
}/*}}}*/
/**
* The pth percentile is the value such that p% of the a sorted data set
* is smaller than it, and (100 - p)% of the data is larger.
*
* A quick algorithm to pick the appropriate value from a sorted data
* set is as follows:
*
* - Count the number of values: n
* - Calculate the position of the value in the data list: i = p * (n + 1)
* - if i is an integer, return the data at that position
* - if i < 1, return the minimum of the data set
* - if i > n, return the maximum of the data set
* - otherwise, average the entries at adjacent positions to i
*
* The median is the 50th percentile value.
*
* @todo need to double check generality of the algorithm
*
* @access public
* @param numeric $p the percentile to estimate, e.g. 25 for 25th percentile
* @return mixed a numeric value on success, a PEAR_Error otherwise
* @see quartiles()
* @see median()
*/
function percentile($p) {/*{{{*/
$count = $this->count();
if (PEAR::isError($count)) {
return $count;
}
if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
$data =& $this->_dataExpanded;
} else {
$data =& $this->_data;
}
$obsidx = $p * ($count + 1) / 100;
if (intval($obsidx) == $obsidx) {
return $data[($obsidx - 1)];
} elseif ($obsidx < 1) {
return $data[0];
} elseif ($obsidx > $count) {
return $data[($count - 1)];
} else {
$left = floor($obsidx - 1);
$right = ceil($obsidx - 1);
return ($data[$left] + $data[$right]) / 2;
}
}/*}}}*/
// private methods
/**
* Utility function to calculate: SUM { (xi - mean)^n }
*
* @access private
* @param numeric $power the exponent
* @param optional double $mean the data set mean value
* @return mixed the sum on success, a PEAR_Error object otherwise
*
* @see stDev()
* @see variaceWithMean();
* @see skewness();
* @see kurtosis();
*/
function __sumdiff($power, $mean=null) {/*{{{*/
if ($this->_data == null) {
return PEAR::raiseError('data has not been set');
}
if (is_null($mean)) {
$mean = $this->mean();
if (PEAR::isError($mean)) {
return $mean;
}
}
$sdiff = 0;
if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
foreach ($this->_data as $val=>$freq) {
$sdiff += $freq * pow((double)($val - $mean), (double)$power);
}
} else {
foreach ($this->_data as $val)
$sdiff += pow((double)($val - $mean), (double)$power);
}
return $sdiff;
}/*}}}*/
/**
* Utility function to calculate the variance with or without
* a fixed mean
*
* @access private
* @param $mean the fixed mean to use, null as default
* @return mixed a numeric value on success, a PEAR_Error otherwise
* @see variance()
* @see varianceWithMean()
*/
function __calcVariance($mean = null) {/*{{{*/
if ($this->_data == null) {
return PEAR::raiseError('data has not been set');
}
$sumdiff2 = $this->__sumdiff(2, $mean);
if (PEAR::isError($sumdiff2)) {
return $sumdiff2;
}
$count = $this->count();
if (PEAR::isError($count)) {
return $count;
}
if ($count == 1) {
return PEAR::raiseError('cannot calculate variance of a singe data point');
}
return ($sumdiff2 / ($count - 1));
}/*}}}*/
/**
* Utility function to calculate the absolute deviation with or without
* a fixed mean
*
* @access private
* @param $mean the fixed mean to use, null as default
* @return mixed a numeric value on success, a PEAR_Error otherwise
* @see absDev()
* @see absDevWithMean()
*/
function __calcAbsoluteDeviation($mean = null) {/*{{{*/
if ($this->_data == null) {
return PEAR::raiseError('data has not been set');
}
$count = $this->count();
if (PEAR::isError($count)) {
return $count;
}
$sumabsdev = $this->__sumabsdev($mean);
if (PEAR::isError($sumabsdev)) {
return $sumabsdev;
}
return $sumabsdev / $count;
}/*}}}*/
/**
* Utility function to calculate: SUM { | xi - mean | }
*
* @access private
* @param optional double $mean the mean value for the set or population
* @return mixed the sum on success, a PEAR_Error object otherwise
*
* @see absDev()
* @see absDevWithMean()
*/
function __sumabsdev($mean=null) {/*{{{*/
if ($this->_data == null) {
return PEAR::raiseError('data has not been set');
}
if (is_null($mean)) {
$mean = $this->mean();
}
$sdev = 0;
if ($this->_dataOption == STATS_DATA_CUMMULATIVE) {
foreach ($this->_data as $val=>$freq) {
$sdev += $freq * abs($val - $mean);
}
} else {
foreach ($this->_data as $val) {
$sdev += abs($val - $mean);
}
}
return $sdev;
}/*}}}*/
/**
* Utility function to format a PEAR_Error to be used by calc(),
* calcBasic() and calcFull()
*
* @access private
* @param mixed $v value to be formatted
* @param boolean $returnErrorObject whether the raw PEAR_Error (when true, default),
* or only the error message will be returned (when false)
* @return mixed if the value is a PEAR_Error object, and $useErrorObject
* is false, then a string with the error message will be returned,
* otherwise the value will not be modified and returned as passed.
*/
function __format($v, $useErrorObject=true) {/*{{{*/
if (PEAR::isError($v) && $useErrorObject == false) {
return $v->getMessage();
} else {
return $v;
}
}/*}}}*/
/**
* Utility function to validate the data and modify it
* according to the current null handling option
*
* @access private
* @return mixed true on success, a PEAR_Error object otherwise
*
* @see setData()
*/
function _validate() {/*{{{*/
$flag = ($this->_dataOption == STATS_DATA_CUMMULATIVE);
foreach ($this->_data as $key=>$value) {
$d = ($flag) ? $key : $value;
$v = ($flag) ? $value : $key;
if (!is_numeric($d)) {
switch ($this->_nullOption) {
case STATS_IGNORE_NULL :
unset($this->_data["$key"]);
break;
case STATS_USE_NULL_AS_ZERO:
if ($flag) {
unset($this->_data["$key"]);
$this->_data[0] += $v;
} else {
$this->_data[$key] = 0;
}
break;
case STATS_REJECT_NULL :
default:
return PEAR::raiseError('data rejected, contains NULL values');
break;
}
}
}
if ($flag) {
ksort($this->_data);
$this->_dataExpanded = array();
foreach ($this->_data as $val=>$freq) {
$this->_dataExpanded = array_pad($this->_dataExpanded, count($this->_dataExpanded) + $freq, $val);
}
sort($this->_dataExpanded);
} else {
sort($this->_data);
}
return true;
}/*}}}*/
}/*}}}*/
// vim: ts=4:sw=4:et:
// vim6: fdl=1: fdm=marker:
?>
