F_inverse_cdf

Evaluates the inverse of the F distribution function.

Synopsis

#include <imsl.h>

float imsl_f_F_inverse_cdf (float p, float df_numerator, float df_denominator)

The type double function is imsl_d_F_inverse_cdf.

Required Arguments

float p (Input)
Probability for which the inverse of the F distribution function is to be evaluated. The argument p must be in the open interval (0.0, 1.0).

float df_numerator (Input)
Numerator degrees of freedom. Argument df_numerator must be positive.

float df_denominator (Input)
Denominator degrees of freedom. Argument df_denominator must be positive.

Return Value

The value of the inverse of the F distribution function evaluated at p. The probability that an F random variable takes a value less than or equal to imsl_f_F_inverse_cdf is p.

Description

The function imsl_f_F_inverse_cdf evaluates the inverse distribution function of a Snedecor’s F random variable with ν1 = df_numerator numerator degrees of freedom and ν2 = df_denominator denominator degrees of freedom. The function is evaluated by making a transformation to a beta random variable and then by evaluating the inverse of an 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. If P ≤ 0.5, imsl_f_F_inverse_cdf uses this relationship directly; otherwise, it also uses a relationship between F random variables that can be expressed as follows:

FF(f, ν1, ν2) = 1 − FF(1/f, ν2 , ν1)

Example

In this example, the 99-th percentage point is calculated for an F random variable with seven degrees of freedom. The same calculation is made for a similar variable with one degree of freedom.

 

#include <imsl.h>

#include <stdio.h>

 

int main()

{

float df_denominator = 1.0;

float df_numerator = 7.0;

float f;

float p = 0.99;

 

f = imsl_f_F_inverse_cdf(p, df_numerator, df_denominator);

printf("The F(7,1) 0.01 critical value is %6.3f\n", f);

}

Output

 

The F(7,1) 0.01 critical value is 5928.370

Fatal Errors

IMSL_F_INVERSE_OVERFLOW

Function imsl_f_F_inverse_cdf is set to machine infinity since overflow would occur upon modifying the inverse value for the F distribution with the result obtained from the inverse beta distribution.