Cdf.ComplementaryF Method

Calculates the complement of the F distribution function.

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

Parameters

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

Return Value

A double specifying the probability that an F random variable takes on a value greater than x.

Remarks

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 Beta. If X is an F variate with and degrees of freedom and , then Y is a beta variate with parameters and . 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 ComplementaryF Distribution Function

Cdf.ComplementaryF Method

Parameters

Return Value

Remarks

See Also