Cdf.ComplementaryF Method

Calculates the complement of the F distribution function.

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0

Syntax

public static double ComplementaryF(
	double x,
	double dfn,
	double dfd
)

Public Shared Function ComplementaryF ( 
	x As Double,
	dfn As Double,
	dfd As Double
) As Double

public:
static double ComplementaryF(
	double x, 
	double dfn, 
	double dfd
)

static member ComplementaryF : 
        x : float * 
        dfn : float * 
        dfd : float -> float

Parameters

x: Type: System.Double
A double, the argument at which $Pr\left(x\gt F\right)$ is to be evaluated.
dfn: Type: System.Double
A double, the numerator degrees of freedom. It must be positive.
dfd: Type: System.Double
A double, the denominator degrees of freedom. It must be positive.

Return Value

Type: Double
A double, the probability that an F random variable takes on a value greater than x.

Remarks

Cdf.ComplementaryF evaluates one minus the distribution function of a Snedecor's F random variable with dfn numerator degrees of freedom and dfd denominator degrees of freedom. The function is evaluated by making a transformation to a beta random variable and then using the function Cdf.Beta. If X is an F variate with and degrees of freedom and , then Y is a beta variate with parameters and . Cdf.ComplementaryF also uses a relationship between F random variables that can be expressed as follows:

${\rm F}(X,{\it dfn},{\it dfd})={\rm F} (1/X,{\it dfd},{\it dfn})$

This function provides higher right tail accuracy for the F distribution.

Plot of F Distribution Function

Reference

Cdf Class

Imsl.Stat Namespace