gamma_inverse_cdf

Evaluates the inverse of the gamma distribution function.

Synopsis

#include <imsls.h>

floatimsls_f_gamma_inverse_cdf (floatp, floata)

The type doublefunction is imsls_d_gamma_inverse_cdf.

Required Arguments

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

floata (Input)
The shape parameter of the gamma distribution. This parameter must be positive.

Return Value

The probability that a gamma random variable takes a value less than or equal to the returned value is p.

Description

Function imsls_f_gamma_inverse_cdf evaluates the inverse distribution function of a gamma random variable with shape parameter a, that is, it determines x (=imsls_f_gamma_inverse_cdf (p, a)), such that

 

where Γ(⋅) is the gamma function. In other words:

 

The probability that the random variable takes a value less than or equal to x is P. See the documentation for function imsls_f_gamma_cdf for further discussion of the gamma distribution.

Function imsls_f_gamma_inverse_cdf uses bisection and modified regula falsi to invert the distribution function, which is evaluated using function imsls_f_gamma_cdf.

Example

In this example, we find the 95-th percentage point for a gamma random variable with shape parameter of 4.

 

 

#include <imsls.h>

#include <stdio.h>

 

int main()

{

    float p = .95, a = 4.0, x;

 

    x = imsls_f_gamma_inverse_cdf(p,a);

    printf("The %4.2f gamma(%1.0f) critical value is %6.4f\n",

        1.0 - p, a, x);

}

Output

 

The 0.05 gamma(4) critical value is 7.7537