<?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\Functions;
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use PhpOffice\PhpSpreadsheet\Calculation\Information\ExcelError;
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use PhpOffice\PhpSpreadsheet\Calculation\Statistical\Averages;
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use PhpOffice\PhpSpreadsheet\Calculation\Statistical\StandardDeviations;
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class StandardNormal
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{
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use ArrayEnabled;
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/**
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* NORMSDIST.
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*
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* Returns the standard normal cumulative distribution function. The distribution has
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* a mean of 0 (zero) and a standard deviation of one. Use this function in place of a
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* table of standard normal curve areas.
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*
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* NOTE: We don't need to check for arrays to array-enable this function, because that is already
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* handled by the logic in Normal::distribution()
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* All we need to do is pass the value through as scalar or as array.
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*
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* @param mixed $value Float value for which we want the probability
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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 cumulative(mixed $value)
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{
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return Normal::distribution($value, 0, 1, true);
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}
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/**
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* NORM.S.DIST.
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*
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* Returns the standard normal cumulative distribution function. The distribution has
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* a mean of 0 (zero) and a standard deviation of one. Use this function in place of a
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* table of standard normal curve areas.
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*
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* NOTE: We don't need to check for arrays to array-enable this function, because that is already
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* handled by the logic in Normal::distribution()
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* All we need to do is pass the value and cumulative through as scalar or as array.
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*
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* @param mixed $value Float value for which we want the probability
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* Or can be an array of values
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* @param mixed $cumulative Boolean value indicating if we want the cdf (true) or the pdf (false)
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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 $cumulative)
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{
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return Normal::distribution($value, 0, 1, $cumulative);
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}
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/**
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* NORMSINV.
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*
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* Returns the inverse of the standard normal cumulative distribution
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*
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* @param mixed $value float probability for which we want the value
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* Or can be an array of values
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*
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* NOTE: We don't need to check for arrays to array-enable this function, because that is already
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* handled by the logic in Normal::inverse()
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* All we need to do is pass the value through as scalar or as array
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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 $value)
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{
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return Normal::inverse($value, 0, 1);
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}
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/**
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* GAUSS.
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*
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* Calculates the probability that a member of a standard normal population will fall between
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* the mean and z standard deviations from the mean.
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*
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* @param mixed $value 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 gauss(mixed $value): array|string|float
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{
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if (is_array($value)) {
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return self::evaluateSingleArgumentArray([self::class, __FUNCTION__], $value);
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}
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if (!is_numeric($value)) {
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return ExcelError::VALUE();
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}
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/** @var float $dist */
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$dist = self::distribution($value, true);
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return $dist - 0.5;
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}
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/**
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* ZTEST.
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*
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* Returns the one-tailed P-value of a z-test.
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*
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* For a given hypothesized population mean, x, Z.TEST returns the probability that the sample mean would be
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* greater than the average of observations in the data set (array) — that is, the observed sample mean.
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*
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* @param mixed $dataSet The dataset should be an array of float values for the observations
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* @param mixed $m0 Alpha Parameter
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* Or can be an array of values
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* @param mixed $sigma A null or float value for the Beta (Standard Deviation) Parameter;
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* if null, we use the standard deviation of the dataset
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* Or can be an array of values
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*
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* @return array|float|string (string if result is 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 zTest(mixed $dataSet, mixed $m0, mixed $sigma = null)
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{
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if (is_array($m0) || is_array($sigma)) {
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return self::evaluateArrayArgumentsSubsetFrom([self::class, __FUNCTION__], 1, $dataSet, $m0, $sigma);
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}
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$dataSet = Functions::flattenArrayIndexed($dataSet);
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if (!is_numeric($m0) || ($sigma !== null && !is_numeric($sigma))) {
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return ExcelError::VALUE();
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}
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if ($sigma === null) {
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/** @var float $sigma */
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$sigma = StandardDeviations::STDEV($dataSet);
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}
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$n = count($dataSet);
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$sub1 = Averages::average($dataSet);
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if (!is_numeric($sub1)) {
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return $sub1;
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}
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$temp = self::cumulative(($sub1 - $m0) / ($sigma / sqrt($n)));
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return 1 - (is_numeric($temp) ? $temp : 0);
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}
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}
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