PHP 클래스 MathPHP\Probability\Distribution\Continuous\NoncentralT

상속: extends Continuous

공개 메소드들

메소드	설명
CDF ( number $x, integer $ν, number $μ ) : number	Cumulative distribution function
PDF ( number $x, integer $ν, $μ ) : number	Probability density function
mean ( integer $ν, number $μ ) : number	Mean of the distribution _ ν Γ((ν - 1)/2) E[T] = μ / - ------------ if ν > 1 √ 2 Γ(ν/2)

비공개 메소드들

메소드	설명
F ( number $x, integer $ν, number $μ ) : number	F used within CDF _ _ 1 ∞ \| / 1 ν \ / ν \ \| Fᵥ,ᵤ(x) = Φ(-μ) + - ∑ \| pⱼIy \| j + -, - \| + qⱼIy \| j + 1, - \| \| 2 ʲ⁼⁰ \|_ \ 2 2 / \ 2 / _\|

메소드 상세

CDF() 공개 정적인 메소드

Fᵥ,ᵤ(x) = Fᵥ,ᵤ(x), if x ≥ 0 = 1 - Fᵥ,₋ᵤ(x) if x < 0

public static CDF ( number $x, integer $ν, number $μ ) : number
$x	number
$ν	integer	Degrees of freedom
$μ	number	Noncentrality parameter
리턴	number

PDF() 공개 정적인 메소드

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
리턴	number

mean() 공개 정적인 메소드

= Does not exist if ν ≤ 1

public static mean ( integer $ν, number $μ ) : number
$ν	integer	Degrees of freedom
$μ	number	Noncentrality parameter
리턴	number