| public static sampleSkewness ( array $X ) : number | ||
| $X | array | list of numbers (random variable X) |
| return | number | |
public static function sampleSkewness(array $X)
{
if (empty($X)) {
return null;
}
$n = count($X);
$μ₃ = self::centralMoment($X, 3);
$μ₂ = self::centralMoment($X, 2);
$μ₂³′² = pow($μ₂, 3 / 2);
$√⟮n⟮n − 1⟯⟯ = sqrt($n * ($n - 1));
return $μ₃ / $μ₂³′² * ($√⟮n⟮n − 1⟯⟯ / ($n - 2));
}