MathPHP\Probability\Distribution\Continuous\NoncentralT::PDF PHP Метод

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PDF() публичный статический Метод

v\ / μ²\ | - | |-1*--- | / ν 3 μ²x² \ / ν + 1 1 μ²x² \ \ \2/ \ 2 / / ₁F₁| - ; - ; --------- | ₁F₁| ----- ; - ; --------- | | ν * Γ(ν + 1) * e | \ 2 2 2(ν + x²)/ \ 2 2 2(ν + x²)/ | --------------------------------- * | √2*μ*x * --------------------------- + -------------------------------- | ν (ν / 2) | / ν + 1 \ / ν \ | 2 * (ν + x²) * Γ(ν / 2) | (ν + x²) * Γ| ------ | √(ν + x²) * Γ| - + 1 | | \ \ 2 / \ 2 / /

public static PDF ( number $x, integer $ν, $μ ) : number
$x	number	percentile
$ν	integer	degrees of freedom > 0
Результат	number

    public static function PDF($x, int $ν, $μ)
    {
        Support::checkLimits(self::LIMITS, ['x' => $x, 'ν' => $ν, 'μ' => $μ]);
        $part1 = $ν ** ($ν / 2) * Special::gamma($ν + 1) * exp(-1 * $μ ** 2 / 2) / 2 ** $ν / ($ν + $x ** 2) ** ($ν / 2) / Special::gamma($ν / 2);
        $F1 = $ν / 2 + 1;
        $F2 = 3 / 2;
        $F3 = $μ ** 2 * $x ** 2 / 2 / ($ν + $x ** 2);
        $inner_part1 = sqrt(2) * $μ * $x * Special::confluentHypergeometric($F1, $F2, $F3) / ($ν + $x ** 2) / Special::gamma(($ν + 1) / 2);
        $F1 = ($ν + 1) / 2;
        $F2 = 1 / 2;
        $inner_part2 = Special::confluentHypergeometric($F1, $F2, $F3) / sqrt($ν + $x ** 2) / Special::gamma($ν / 2 + 1);
        return $part1 * ($inner_part1 + $inner_part2);
    }

NoncentralT

CDF

PDF

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