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<?php
namespace PhpOffice\PhpSpreadsheet\Calculation\Statistical\Distributions;
use PhpOffice\PhpSpreadsheet\Calculation\ArrayEnabled;
use PhpOffice\PhpSpreadsheet\Calculation\Functions;
use PhpOffice\PhpSpreadsheet\Calculation\Information\ExcelError;
use PhpOffice\PhpSpreadsheet\Calculation\Statistical\Averages;
use PhpOffice\PhpSpreadsheet\Calculation\Statistical\StandardDeviations;
class StandardNormal
{
use ArrayEnabled;
/**
* 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.
*
* NOTE: We don't need to check for arrays to array-enable this function, because that is already
* handled by the logic in Normal::distribution()
* All we need to do is pass the value through as scalar or as array.
*
* @param mixed $value Float value for which we want the probability
* Or can be an array of values
*
* @return array|float|string The result, or a string containing an error
* If an array of numbers is passed as an argument, then the returned result will also be an array
* with the same dimensions
*/
public static function cumulative($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.
*
* NOTE: We don't need to check for arrays to array-enable this function, because that is already
* handled by the logic in Normal::distribution()
* All we need to do is pass the value and cumulative through as scalar or as array.
*
* @param mixed $value Float value for which we want the probability
* Or can be an array of values
* @param mixed $cumulative Boolean value indicating if we want the cdf (true) or the pdf (false)
* Or can be an array of values
*
* @return array|float|string The result, or a string containing an error
* If an array of numbers is passed as an argument, then the returned result will also be an array
* with the same dimensions
*/
public static function distribution($value, $cumulative)
{
return Normal::distribution($value, 0, 1, $cumulative);
}
/**
* NORMSINV.
*
* Returns the inverse of the standard normal cumulative distribution
*
* @param mixed $value float probability for which we want the value
* Or can be an array of values
*
* NOTE: We don't need to check for arrays to array-enable this function, because that is already
* handled by the logic in Normal::inverse()
* All we need to do is pass the value through as scalar or as array
*
* @return array|float|string The result, or a string containing an error
* If an array of numbers is passed as an argument, then the returned result will also be an array
* with the same dimensions
*/
public static function inverse($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 $value
* Or can be an array of values
*
* @return array|float|string The result, or a string containing an error
* If an array of numbers is passed as an argument, then the returned result will also be an array
* with the same dimensions
*/
public static function gauss($value)
{
if (is_array($value)) {
return self::evaluateSingleArgumentArray([self::class, __FUNCTION__], $value);
}
if (!is_numeric($value)) {
return ExcelError::VALUE();
}
/** @var float */
$dist = self::distribution($value, true);
return $dist - 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
* Or can be an array of values
* @param mixed $sigma A null or float value for the Beta (Standard Deviation) Parameter;
* if null, we use the standard deviation of the dataset
* Or can be an array of values
*
* @return array|float|string (string if result is an error)
* If an array of numbers is passed as an argument, then the returned result will also be an array
* with the same dimensions
*/
public static function zTest($dataSet, $m0, $sigma = null)
{
if (is_array($m0) || is_array($sigma)) {
return self::evaluateArrayArgumentsSubsetFrom([self::class, __FUNCTION__], 1, $dataSet, $m0, $sigma);
}
$dataSet = Functions::flattenArrayIndexed($dataSet);
if (!is_numeric($m0) || ($sigma !== null && !is_numeric($sigma))) {
return ExcelError::VALUE();
}
if ($sigma === null) {
/** @var float */
$sigma = StandardDeviations::STDEV($dataSet);
}
$n = count($dataSet);
return 1 - self::cumulative((Averages::average($dataSet) - $m0) / ($sigma / sqrt($n)));
}
}
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