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<?php
namespace PhpOffice\PhpSpreadsheet\Calculation\Statistical\Distributions;
use PhpOffice\PhpSpreadsheet\Calculation\Functions;
use PhpOffice\PhpSpreadsheet\Calculation\Statistical\Averages;
use PhpOffice\PhpSpreadsheet\Calculation\Statistical\StandardDeviations;
class StandardNormal
{
/**
* NORMSDIST.
*
* Returns the standard normal cumulative distribution function. The distribution has
* a mean of 0 (zero) and a standard deviation of one. Use this function in place of a
* table of standard normal curve areas.
*
* @param mixed $value Float value for which we want the probability
*
* @return float|string The result, or a string containing an error
*/
public static function cumulative($value)
{
return Normal::distribution($value, 0, 1, true);
}
/**
* NORM.S.DIST.
*
* Returns the standard normal cumulative distribution function. The distribution has
* a mean of 0 (zero) and a standard deviation of one. Use this function in place of a
* table of standard normal curve areas.
*
* @param mixed $value Float value for which we want the probability
* @param mixed $cumulative Boolean value indicating if we want the cdf (true) or the pdf (false)
*
* @return float|string The result, or a string containing an error
*/
public static function distribution($value, $cumulative)
{
return Normal::distribution($value, 0, 1, $cumulative);
}
/**
* NORMSINV.
*
* Returns the inverse of the standard normal cumulative distribution
*
* @param mixed $value Float probability for which we want the value
*
* @return float|string The result, or a string containing an error
*/
public static function inverse($value)
{
return Normal::inverse($value, 0, 1);
}
/**
* GAUSS.
*
* Calculates the probability that a member of a standard normal population will fall between
* the mean and z standard deviations from the mean.
*
* @param mixed $value
*
* @return float|string The result, or a string containing an error
*/
public static function gauss($value)
{
$value = Functions::flattenSingleValue($value);
if (!is_numeric($value)) {
return Functions::VALUE();
}
return self::distribution($value, true) - 0.5;
}
/**
* ZTEST.
*
* Returns the one-tailed P-value of a z-test.
*
* For a given hypothesized population mean, x, Z.TEST returns the probability that the sample mean would be
* greater than the average of observations in the data set (array) — that is, the observed sample mean.
*
* @param mixed $dataSet The dataset should be an array of float values for the observations
* @param mixed $m0 Alpha Parameter
* @param mixed $sigma A null or float value for the Beta (Standard Deviation) Parameter;
* if null, we use the standard deviation of the dataset
*
* @return float|string (string if result is an error)
*/
public static function zTest($dataSet, $m0, $sigma = null)
{
$dataSet = Functions::flattenArrayIndexed($dataSet);
$m0 = Functions::flattenSingleValue($m0);
$sigma = Functions::flattenSingleValue($sigma);
if (!is_numeric($m0) || ($sigma !== null && !is_numeric($sigma))) {
return Functions::VALUE();
}
if ($sigma === null) {
$sigma = StandardDeviations::STDEV($dataSet);
}
$n = count($dataSet);
return 1 - self::cumulative((Averages::average($dataSet) - $m0) / ($sigma / sqrt($n)));
}
}