F_cdf

Evaluates the F distribution function.

Synopsis

#include <imsl.h>

float imsl_f_F_cdf (float f, float df_denominator, float df_numerator)

The type double function is imsl_d_F_cdf.

Required Arguments

float f (Input)
Point at which the F distribution function is to be evaluated.

float df_numerator (Input)
The numerator degrees of freedom. The argument df_numerator must be positive.

float df_denominator (Input)
The denominator degrees of freedom. The argument df_denominator must be positive.

Return Value

The probability that an F random variable takes a value less than or equal to the input point, f.

Description

The function imsl_f_F_cdf evaluates the distribution function of a Snedecor’s F random variable with df_numerator and df_denominator. The function is evaluated by making a transformation to a beta random variable and then by evaluating the incomplete beta function. If X is an F variate with ν1 and ν2 degrees of freedom and Y = (ν1 X)/(ν2 + ν1 X), then Y is a beta variate with parameters p = ν1/2 and q = ν2/2.

The function imsl_f_F_cdf also uses a relationship between F random variables that can be expressed as follows:

FF(f, ν1, ν2) = 1 − FF(1/f, ν2, ν1) where FF is the distribution function for an F random variable.

 

Figure 1,  Plot of FF (f, 1.0, 1.0)

Example

This example finds the probability that an F random variable with one numerator and one denominator degree of freedom is greater than 648.

 

#include <imsl.h>

#include <stdio.h>

 

int main()

{

float p;

float F = 648.0;

float df_numerator = 1.0;

float df_denominator = 1.0;

 

p = 1.0 - imsl_f_F_cdf(F,df_numerator, df_denominator);

printf("%s %s %6.4f.\n", "The probability that an F(1,1) variate",

"is greater than 648 is", p);

}

Output

 

The probability that an F(1,1) variate is greater than 648 is 0.0250.