complementary_F_cdf
Evaluates the complement of the F distribution function.
Synopsis
#include <imsls.h>
float imsls_f_complementary_F_cdf (float f, float df_numerator, float df_denominator)
The type double function is imsls_d_complementary_F_cdf.
Required Arguments
float f (Input)
Argument for which Pr(x > f) is to be evaluated.
Argument for which Pr(x > f) is to be evaluated.
float df_numerator (Input)
The numerator degrees of freedom. Argument df_numerator must be positive.
The numerator degrees of freedom. Argument df_numerator must be positive.
float df_denominator (Input)
The denominator degrees of freedom. Argument df_denominator must be positive.
The denominator degrees of freedom. Argument df_denominator must be positive.
Return Value
The probability that an F random variable takes a value greater than f.
Description
Function imsls_f_complementary_F_cdf evaluates one minus 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, then evaluating the incomplete beta function. If X is an F variate with ν1 and ν2 degrees of freedom and Y = (ν1X)/(ν2 + ν1X), then Y is a beta variate with parameters p = ν1/2 and q= ν2/2. Function imsls_f_comlementary_F_cdf also uses a relationship between F random variables that can be expressed as
where FF is the distribution function for an F random variable.
This function provides higher right tail accuracy for the F distribution.
Figure 17, Plot of FF(f/df_n, df_d)
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 <imsls.h>
#include <stdio.h>
int main()
{
float F = 648.0, df_numerator = 1.0, df_denominator = 1.0, p;
p = imsls_f_complementary_F_cdf(F,df_numerator, df_denominator);
printf("The probability that an F(%2.1f,%2.1f) variate is greater",
df_numerator, df_denominator);
printf(" than %5.1f is %6.4f.\n", F, p);
}
Output
The probability that an F(1.0,1.0) variate is greater than 648.0 is 0.0250.
