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Diffstat (limited to 'admin/survey/excel/PHPExcel/Shared/JAMA/examples/Stats.php')
| -rw-r--r-- | admin/survey/excel/PHPExcel/Shared/JAMA/examples/Stats.php | 1605 |
1 files changed, 1605 insertions, 0 deletions
diff --git a/admin/survey/excel/PHPExcel/Shared/JAMA/examples/Stats.php b/admin/survey/excel/PHPExcel/Shared/JAMA/examples/Stats.php new file mode 100644 index 0000000..7d1359b --- /dev/null +++ b/admin/survey/excel/PHPExcel/Shared/JAMA/examples/Stats.php @@ -0,0 +1,1605 @@ +<?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:
+
+?>
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