/**
* Cumulative distribution function
*
* Cumulative t value up to a point, left tail.
*
* / k x \
* γ | - , - |
* \ 2 2 /
* CDF = -------------
* / k \
* Γ | - |
* \ 2 /
*
* @param number $x Chi-square critical value (CV) > 0
* @param int $k degrees of freedom > 0
*
* @return number cumulative probability
*/
public static function CDF($x, int $k)
{
Support::checkLimits(self::LIMITS, ['x' => $x, 'k' => $k]);
// Numerator
$γ⟮k/2、x/2⟯ = Special::γ($k / 2, $x / 2);
// Demoninator
$Γ⟮k/2⟯ = Special::Γ($k / 2);
return $γ⟮k/2、x/2⟯ / $Γ⟮k/2⟯;
}