<?php
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namespace PhpOffice\PhpSpreadsheet\Calculation\Statistical\Distributions;
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use PhpOffice\PhpSpreadsheet\Calculation\ArrayEnabled;
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use PhpOffice\PhpSpreadsheet\Calculation\Exception;
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use PhpOffice\PhpSpreadsheet\Calculation\Functions;
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use PhpOffice\PhpSpreadsheet\Calculation\Information\ExcelError;
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class StudentT
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{
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use ArrayEnabled;
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/**
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* TDIST.
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*
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* Returns the probability of Student's T distribution.
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*
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* @param mixed $value Float value for the distribution
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* Or can be an array of values
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* @param mixed $degrees Integer value for degrees of freedom
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* Or can be an array of values
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* @param mixed $tails Integer value for the number of tails (1 or 2)
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* Or can be an array of values
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*
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* @return array|float|string The result, or a string containing an error
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* If an array of numbers is passed as an argument, then the returned result will also be an array
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* with the same dimensions
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*/
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public static function distribution(mixed $value, mixed $degrees, mixed $tails)
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{
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if (is_array($value) || is_array($degrees) || is_array($tails)) {
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return self::evaluateArrayArguments([self::class, __FUNCTION__], $value, $degrees, $tails);
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}
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try {
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$value = DistributionValidations::validateFloat($value);
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$degrees = DistributionValidations::validateInt($degrees);
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$tails = DistributionValidations::validateInt($tails);
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} catch (Exception $e) {
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return $e->getMessage();
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}
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if (($value < 0) || ($degrees < 1) || ($tails < 1) || ($tails > 2)) {
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return ExcelError::NAN();
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}
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return self::calculateDistribution($value, $degrees, $tails);
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}
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/**
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* TINV.
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*
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* Returns the one-tailed probability of the chi-squared distribution.
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*
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* @param mixed $probability Float probability for the function
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* Or can be an array of values
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* @param mixed $degrees Integer value for degrees of freedom
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* Or can be an array of values
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*
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* @return array|float|string The result, or a string containing an error
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* If an array of numbers is passed as an argument, then the returned result will also be an array
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* with the same dimensions
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*/
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public static function inverse(mixed $probability, mixed $degrees)
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{
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if (is_array($probability) || is_array($degrees)) {
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return self::evaluateArrayArguments([self::class, __FUNCTION__], $probability, $degrees);
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}
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try {
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$probability = DistributionValidations::validateProbability($probability);
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$degrees = DistributionValidations::validateInt($degrees);
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} catch (Exception $e) {
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return $e->getMessage();
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}
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if ($degrees <= 0) {
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return ExcelError::NAN();
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}
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$callback = fn ($value) => self::distribution($value, $degrees, 2);
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$newtonRaphson = new NewtonRaphson($callback);
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return $newtonRaphson->execute($probability);
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}
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private static function calculateDistribution(float $value, int $degrees, int $tails): float
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{
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// tdist, which finds the probability that corresponds to a given value
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// of t with k degrees of freedom. This algorithm is translated from a
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// pascal function on p81 of "Statistical Computing in Pascal" by D
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// Cooke, A H Craven & G M Clark (1985: Edward Arnold (Pubs.) Ltd:
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// London). The above Pascal algorithm is itself a translation of the
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// fortran algoritm "AS 3" by B E Cooper of the Atlas Computer
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// Laboratory as reported in (among other places) "Applied Statistics
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// Algorithms", editied by P Griffiths and I D Hill (1985; Ellis
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// Horwood Ltd.; W. Sussex, England).
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$tterm = $degrees;
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$ttheta = atan2($value, sqrt($tterm));
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$tc = cos($ttheta);
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$ts = sin($ttheta);
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if (($degrees % 2) === 1) {
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$ti = 3;
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$tterm = $tc;
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} else {
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$ti = 2;
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$tterm = 1;
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}
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$tsum = $tterm;
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while ($ti < $degrees) {
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$tterm *= $tc * $tc * ($ti - 1) / $ti;
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$tsum += $tterm;
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$ti += 2;
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}
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$tsum *= $ts;
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if (($degrees % 2) == 1) {
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$tsum = Functions::M_2DIVPI * ($tsum + $ttheta);
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}
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$tValue = 0.5 * (1 + $tsum);
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if ($tails == 1) {
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return 1 - abs($tValue);
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}
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return 1 - abs((1 - $tValue) - $tValue);
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}
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}
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