beta_inverse_cdf

Evaluates the inverse of the beta distribution function.

Synopsis

#include <imsls.h>

float imsls_f_beta_inverse_cdf (float p, float pin, float qin)

The type double function is imsls_d_beta_inverse_cdf.

Required Arguments

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

float pin (Input)
First beta distribution parameter. Argument pin must be positive.

float qin (Input)
Second beta distribution parameter. Argument qin must be positive.

Return Value

Function imsls_f_beta_inverse_cdf returns the inverse distribution function of a beta random variable with parameters pin and qin.

Description

With P = p, p = pin, and q = qin, the beta_inverse_cdf returns x 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.

Example

Suppose X is a beta random variable with parameters 12 and 12 (X has a symmetric distribution). In this example, we find the value x such that the probability that X is less than or equal to x is 0.9.

 

#include <imsls.h>

#include <stdio.h>

 

int main()

{

    float  pin = 12.0, qin = 12.0, p = 0.9, x;

 

    x = imsls_f_beta_inverse_cdf(p, pin, qin);

    printf(" X is less than %6.4f with "

        "probability %3.1f.\n", x, p);

}

Output

 

X is less than 0.6299 with probability 0.9.