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<?php
namespace PhpOffice\PhpSpreadsheet\Calculation\Statistical\Distributions;
use PhpOffice\PhpSpreadsheet\Calculation\ArrayEnabled;
use PhpOffice\PhpSpreadsheet\Calculation\Engineering;
use PhpOffice\PhpSpreadsheet\Calculation\Exception;
use PhpOffice\PhpSpreadsheet\Calculation\Information\ExcelError;
class Normal
{
use ArrayEnabled;
public const SQRT2PI = 2.5066282746310005024157652848110452530069867406099;
/**
* NORMDIST.
*
* Returns the normal distribution for the specified mean and standard deviation. This
* function has a very wide range of applications in statistics, including hypothesis
* testing.
*
* @param mixed $value Float value for which we want the probability
* Or can be an array of values
* @param mixed $mean Mean value as a float
* Or can be an array of values
* @param mixed $stdDev Standard Deviation as a float
* 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, $mean, $stdDev, $cumulative)
{
if (is_array($value) || is_array($mean) || is_array($stdDev) || is_array($cumulative)) {
return self::evaluateArrayArguments([self::class, __FUNCTION__], $value, $mean, $stdDev, $cumulative);
}
try {
$value = DistributionValidations::validateFloat($value);
$mean = DistributionValidations::validateFloat($mean);
$stdDev = DistributionValidations::validateFloat($stdDev);
$cumulative = DistributionValidations::validateBool($cumulative);
} catch (Exception $e) {
return $e->getMessage();
}
if ($stdDev < 0) {
return ExcelError::NAN();
}
if ($cumulative) {
return 0.5 * (1 + Engineering\Erf::erfValue(($value - $mean) / ($stdDev * sqrt(2))));
}
return (1 / (self::SQRT2PI * $stdDev)) * exp(0 - (($value - $mean) ** 2 / (2 * ($stdDev * $stdDev))));
}
/**
* NORMINV.
*
* Returns the inverse of the normal cumulative distribution for the specified mean and standard deviation.
*
* @param mixed $probability Float probability for which we want the value
* Or can be an array of values
* @param mixed $mean Mean Value as a float
* Or can be an array of values
* @param mixed $stdDev Standard Deviation as a float
* Or can be an array of values
*
* @return array|float|string The result, or a string containing an error
* If an array of numbers is passed as an argument, then the returned result will also be an array
* with the same dimensions
*/
public static function inverse($probability, $mean, $stdDev)
{
if (is_array($probability) || is_array($mean) || is_array($stdDev)) {
return self::evaluateArrayArguments([self::class, __FUNCTION__], $probability, $mean, $stdDev);
}
try {
$probability = DistributionValidations::validateProbability($probability);
$mean = DistributionValidations::validateFloat($mean);
$stdDev = DistributionValidations::validateFloat($stdDev);
} catch (Exception $e) {
return $e->getMessage();
}
if ($stdDev < 0) {
return ExcelError::NAN();
}
return (self::inverseNcdf($probability) * $stdDev) + $mean;
}
/*
* inverse_ncdf.php
* -------------------
* begin : Friday, January 16, 2004
* copyright : (C) 2004 Michael Nickerson
* email : nickersonm@yahoo.com
*
*/
private static function inverseNcdf($p)
{
// Inverse ncdf approximation by Peter J. Acklam, implementation adapted to
// PHP by Michael Nickerson, using Dr. Thomas Ziegler's C implementation as
// a guide. http://home.online.no/~pjacklam/notes/invnorm/index.html
// I have not checked the accuracy of this implementation. Be aware that PHP
// will truncate the coeficcients to 14 digits.
// You have permission to use and distribute this function freely for
// whatever purpose you want, but please show common courtesy and give credit
// where credit is due.
// Input paramater is $p - probability - where 0 < p < 1.
// Coefficients in rational approximations
static $a = [
1 => -3.969683028665376e+01,
2 => 2.209460984245205e+02,
3 => -2.759285104469687e+02,
4 => 1.383577518672690e+02,
5 => -3.066479806614716e+01,
6 => 2.506628277459239e+00,
];
static $b = [
1 => -5.447609879822406e+01,
2 => 1.615858368580409e+02,
3 => -1.556989798598866e+02,
4 => 6.680131188771972e+01,
5 => -1.328068155288572e+01,
];
static $c = [
1 => -7.784894002430293e-03,
2 => -3.223964580411365e-01,
3 => -2.400758277161838e+00,
4 => -2.549732539343734e+00,
5 => 4.374664141464968e+00,
6 => 2.938163982698783e+00,
];
static $d = [
1 => 7.784695709041462e-03,
2 => 3.224671290700398e-01,
3 => 2.445134137142996e+00,
4 => 3.754408661907416e+00,
];
// Define lower and upper region break-points.
$p_low = 0.02425; //Use lower region approx. below this
$p_high = 1 - $p_low; //Use upper region approx. above this
if (0 < $p && $p < $p_low) {
// Rational approximation for lower region.
$q = sqrt(-2 * log($p));
return ((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6]) /
(((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1);
} elseif ($p_high < $p && $p < 1) {
// Rational approximation for upper region.
$q = sqrt(-2 * log(1 - $p));
return -((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6]) /
(((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1);
}
// Rational approximation for central region.
$q = $p - 0.5;
$r = $q * $q;
return ((((($a[1] * $r + $a[2]) * $r + $a[3]) * $r + $a[4]) * $r + $a[5]) * $r + $a[6]) * $q /
((((($b[1] * $r + $b[2]) * $r + $b[3]) * $r + $b[4]) * $r + $b[5]) * $r + 1);
}
}
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