Calculates the complement of the F distribution function.

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0

Syntax

C#
public static double ComplementaryF(
	double x,
	double dfn,
	double dfd
)
Visual Basic (Declaration)
Public Shared Function ComplementaryF ( _
	x As Double, _
	dfn As Double, _
	dfd As Double _
) As Double
Visual C++
public:
static double ComplementaryF(
	double x, 
	double dfn, 
	double dfd
)

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

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 v_1 and v_2 degrees of freedom and Y = v_1X/(v_2 + v_1X), then Y is a beta variate with parameters p=v_1/2 and q = v_2/2. 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

See Also