public static function beta($x, $y) : float
{
if ($x == 0 || $y == 0) {
return \INF;
}
$Γ⟮x⟯Γ⟮y⟯ = self::gamma($x) * self::gamma($y);
$Γ⟮x ＋ y⟯ = self::gamma($x + $y);
return $Γ⟮x⟯Γ⟮y⟯ / $Γ⟮x ＋ y⟯;
} /**
* Probability density function
*
* xᵃ⁻¹(1 - x)ᵝ⁻¹
* pdf = --------------
* B(α,β)
*
* @param number $α shape parameter α > 0
* @param number $β shape parameter β > 0
* @param number $x x ∈ (0,1)
*
* @return float
*/
public static function PDF($x, $α, $β)
{
Support::checkLimits(self::LIMITS, ['x' => $x, 'α' => $α, 'β' => $β]);
$xᵃ⁻¹ = pow($x, $α - 1);
$⟮1 − x⟯ᵝ⁻¹ = pow(1 - $x, $β - 1);
$B⟮α、β⟯ = Special::beta($α, $β);
return $xᵃ⁻¹ * $⟮1 − x⟯ᵝ⁻¹ / $B⟮α、β⟯;
}
