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<?php
namespace PhpOffice\PhpSpreadsheet\Calculation\Statistical\Distributions;
use PhpOffice\PhpSpreadsheet\Calculation\ArrayEnabled;
use PhpOffice\PhpSpreadsheet\Calculation\Exception;
use PhpOffice\PhpSpreadsheet\Calculation\Functions;
use PhpOffice\PhpSpreadsheet\Calculation\Information\ExcelError;
class StudentT
{
use ArrayEnabled;
private const MAX_ITERATIONS = 256;
/**
* TDIST.
*
* Returns the probability of Student's T distribution.
*
* @param mixed $value Float value for the distribution
* Or can be an array of values
* @param mixed $degrees Integer value for degrees of freedom
* Or can be an array of values
* @param mixed $tails Integer value for the number of tails (1 or 2)
* Or can be an array of values
*
* @return array|float|string The result, or a string containing an error
* If an array of numbers is passed as an argument, then the returned result will also be an array
* with the same dimensions
*/
public static function distribution($value, $degrees, $tails)
{
if (is_array($value) || is_array($degrees) || is_array($tails)) {
return self::evaluateArrayArguments([self::class, __FUNCTION__], $value, $degrees, $tails);
}
try {
$value = DistributionValidations::validateFloat($value);
$degrees = DistributionValidations::validateInt($degrees);
$tails = DistributionValidations::validateInt($tails);
} catch (Exception $e) {
return $e->getMessage();
}
if (($value < 0) || ($degrees < 1) || ($tails < 1) || ($tails > 2)) {
return ExcelError::NAN();
}
return self::calculateDistribution($value, $degrees, $tails);
}
/**
* TINV.
*
* Returns the one-tailed probability of the chi-squared distribution.
*
* @param mixed $probability Float probability for the function
* Or can be an array of values
* @param mixed $degrees Integer value for degrees of freedom
* Or can be an array of values
*
* @return array|float|string The result, or a string containing an error
* If an array of numbers is passed as an argument, then the returned result will also be an array
* with the same dimensions
*/
public static function inverse($probability, $degrees)
{
if (is_array($probability) || is_array($degrees)) {
return self::evaluateArrayArguments([self::class, __FUNCTION__], $probability, $degrees);
}
try {
$probability = DistributionValidations::validateProbability($probability);
$degrees = DistributionValidations::validateInt($degrees);
} catch (Exception $e) {
return $e->getMessage();
}
if ($degrees <= 0) {
return ExcelError::NAN();
}
$callback = function ($value) use ($degrees) {
return self::distribution($value, $degrees, 2);
};
$newtonRaphson = new NewtonRaphson($callback);
return $newtonRaphson->execute($probability);
}
/**
* @return float
*/
private static function calculateDistribution(float $value, int $degrees, int $tails)
{
// tdist, which finds the probability that corresponds to a given value
// of t with k degrees of freedom. This algorithm is translated from a
// pascal function on p81 of "Statistical Computing in Pascal" by D
// Cooke, A H Craven & G M Clark (1985: Edward Arnold (Pubs.) Ltd:
// London). The above Pascal algorithm is itself a translation of the
// fortran algoritm "AS 3" by B E Cooper of the Atlas Computer
// Laboratory as reported in (among other places) "Applied Statistics
// Algorithms", editied by P Griffiths and I D Hill (1985; Ellis
// Horwood Ltd.; W. Sussex, England).
$tterm = $degrees;
$ttheta = atan2($value, sqrt($tterm));
$tc = cos($ttheta);
$ts = sin($ttheta);
if (($degrees % 2) === 1) {
$ti = 3;
$tterm = $tc;
} else {
$ti = 2;
$tterm = 1;
}
$tsum = $tterm;
while ($ti < $degrees) {
$tterm *= $tc * $tc * ($ti - 1) / $ti;
$tsum += $tterm;
$ti += 2;
}
$tsum *= $ts;
if (($degrees % 2) == 1) {
$tsum = Functions::M_2DIVPI * ($tsum + $ttheta);
}
$tValue = 0.5 * (1 + $tsum);
if ($tails == 1) {
return 1 - abs($tValue);
}
return 1 - abs((1 - $tValue) - $tValue);
}
}
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