public static function CDF($t, int $ν)
{
Support::checkLimits(self::LIMITS, ['t' => $t, 'ν' => $ν]);
if ($t == 0) {
return 0.5;
}
$x⟮t⟯ = $ν / ($t ** 2 + $ν);
$ν/2 = $ν / 2;
$½ = 0.5;
$Iₓ = Special::regularizedIncompleteBeta($x⟮t⟯, $ν/2, $½);
if ($t < 0) {
return $½ * $Iₓ;
}
// $t ≥ 0
return 1 - $½ * $Iₓ;
}
/** * Cumulative distribution function * * Fᵥ,ᵤ(x) = Fᵥ,ᵤ(x), if x ≥ 0 * = 1 - Fᵥ,₋ᵤ(x) if x < 0 * * @param number $x * @param int $ν Degrees of freedom * @param number $μ Noncentrality parameter * * @return number */ public static function CDF($x, int $ν, $μ) { Support::checkLimits(self::LIMITS, ['x' => $x, 'ν' => $ν, 'μ' => $μ]); if ($μ == 0) { return StudentT::CDF($x, $ν); } if ($x >= 0) { return self::F($x, $ν, $μ); } return 1 - self::F($x, $ν, -$μ); }