Evaluates the hypergeometric distribution function.

Synopsis

#include <imsls.h>

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

The type double function is imsls_d_hypergeometric_cdf.

Required Arguments

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

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

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

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

Return Value

The probability that k or fewer defectives occur in a sample of size n drawn from a lot of size l that contains m defectives.

Description

Function imsls_f_hypergeometric_cdf evaluates the distribution 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 i = max (0, n − l + m).

If k is greater than or equal to i and less than or equal to min (n, m), imsls_f_hypergeometric_cdf sums the terms in this expression for j going from i up to k; otherwise, 0 or 1 is returned, as appropriate. To avoid rounding in the accumulation, imsls_f_hypergeometric_cdf performs the summation differently, depending on whether or not k is greater than the mode of the distribution, which is the greatest integer less than or equal to (m + 1) (n + 1)/(l + 2).

Example

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

#include <imsls.h>

void main()
{
    int         k = 7;
    int         l = 1000;
    int         m = 70;
    int         n = 100;
    float       p;

    p = imsls_f_hypergeometric_cdf(k,n,m,l);
    printf("\nPr (x <= 7) = %6.4f", p);
}

Output

Pr (x <= 7) = 0.599

Informational Errors

IMSLS_LESS_THAN_ZERO                         Since “k” = # is less than zero, the distribution function is set to zero.

IMSLS_K_GREATER_THAN_N                     The input argument, k, is greater than the sample size.

Fatal Errors

IMSLS_LOT_SIZE_TOO_SMALL                Lot size must be greater than or equal to
n and m.

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