hypergeometric_pdf

Evaluates the hypergeometric probability function.

Synopsis

#include <imsls.h>

float imsls_f_hypergeometric_pdf (int k, int n, int m, int l)

The type double function is imsls_d_hypergeometric_pdf.

Required Arguments

int k (Input)
Argument for which the hypergeometric probability function is to be evaluated.

int n (Input)
Sample size. n must be greater than zero and greater than or equal to k.

int m (Input)
Number of defectives in the lot.

int l (Input)
Lot size. l must be greater than or equal to n and m.

Return Value

The probability that a hypergeometric random variable takes a value equal to k. This value is the probability that exactly k defectives occur in a sample of size n drawn from a lot of size l that contains m defectives.

Description

The function imsls_f_hypergeometic_pdf evaluates the probability function of a hypergeometric random variable with parameters n, l, and m. The hypergeometric random variable X can be thought of as the number of items of a given type in a random sample of size n that is drawn without replacement from a population of size l containing m items of this type. The probability function is

 

where

 

and

 

imsls_f_hypergeometic_pdf evaluates the expression using log gamma functions.

Example

Suppose X is a hypergeometric random variable with n = 100, l = 1000, and m = 70. In this example, we evaluate the probability function at 7.

 

#include <imsls.h>

#include <stdio.h>

 

int main()

{

    int    k=7, n = 100, l = 1000, m = 70;

    float  pr;

    pr = imsls_f_hypergeometric_pdf(k, n, m, l);

    printf("The probability that X is equal to "

        "%d is %6.4f\n", k, pr);

}

Output

 

The probability that X is equal to 7 is 0.1628