PHP Class MathPHP\Probability\Distribution\Continuous\StudentT

Inheritance: extends Continuous

Public Methods

Method	Description
CDF ( number $t, integer $ν )	Cumulative distribution function Calculate the cumulative t value up to a point, left tail.
PDF ( number $x, integer $ν )	Probability density function
inverse2Tails ( number $p, number $ν ) : number	Inverse 2 tails Find t such that the area greater than t and the area beneath -t is p.
mean ( number $ν ) : number	Mean of the distribution
median ( number $ν ) : number	Median of the distribution

cdf = 1 - ½Iₓ₍t₎(ν/2, ½) ν where x(t) = ------ t² + ν Iₓ₍t₎(ν/2, ½) is the regularized incomplete beta function

public static CDF ( number $t, integer $ν )
$t	number	t score
$ν	integer	degrees of freedom > 0

ν + 1 \ Γ | ----- | \ 2 / / x² \ ⁻⁽ᵛ⁺¹⁾/² ------------- | 1 + -- | __ / ν \ \ ν / √νπ Γ | - | \ 2 /

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

Inverse 2 tails Find t such that the area greater than t and the area beneath -t is p.

public static inverse2Tails ( number $p, number $ν ) : number
$p	number	Proportion of area
$ν	number	Degrees of freedom
return	number	t-score

μ = 0 if ν > 1 otherwise undefined

public static mean ( number $ν ) : number
$ν	number	Degrees of freedom
return	number

μ = 0

public static median ( number $ν ) : number
$ν	number	Degrees of freedom
return	number