From f1ab2f022fdc780aca0944d90e9a0e844a0820d7 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Anton=20Luka=20=C5=A0ijanec?= Date: Mon, 27 May 2024 13:12:17 +0200 Subject: =?UTF-8?q?2024-02-19:=20popravljen=20(prej=C5=A1nji=20commit=20je?= =?UTF-8?q?=20napa=C4=8Den)?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../excel/PHPExcel/Shared/JAMA/examples/Stats.php | 1605 -------------------- 1 file changed, 1605 deletions(-) delete mode 100644 admin/survey/excel/PHPExcel/Shared/JAMA/examples/Stats.php (limited to 'admin/survey/excel/PHPExcel/Shared/JAMA/examples/Stats.php') diff --git a/admin/survey/excel/PHPExcel/Shared/JAMA/examples/Stats.php b/admin/survey/excel/PHPExcel/Shared/JAMA/examples/Stats.php deleted file mode 100644 index 7d1359b..0000000 --- a/admin/survey/excel/PHPExcel/Shared/JAMA/examples/Stats.php +++ /dev/null @@ -1,1605 +0,0 @@ - | -// +----------------------------------------------------------------------+ -// -// $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: -* -* 
-* $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);
-*
-* -* can be epxressed more compactly as: -* -* 
-* $data2 = array('1'=>9, '2'=>8, '3'=>5, '4.1'=>2);
-*
-* -* Example of use: -* -* 
-* 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'].' 
\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();
-*
-* -* Originally this class was part of NumPHP (Numeric PHP package) -* -* @author Jesus M. Castagnetto -* @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() - * - * 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: - -?> -- cgit v1.2.3