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 9-1 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>
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.
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