hypergeometric_cdf
Evaluates the hypergeometric distribution function.
Synopsis
#include <imsl.h>
float imsl_f_hypergeometric_cdf (int k, int n, int m, int l)
The type double procedure is imsl_d_hypergeometric_cdf.
Required Arguments
int k (Input)
Argument for which the hypergeometric distribution function is to be evaluated.
int n (Input)
Sample size n must be 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 k or fewer defectives occur in a sample of size n drawn from a lot of size l that contains m defectives.
Description
The function imsl_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), imsl_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, imsl_f_hypergeometric_cdf performs the summation differently, depending on whether k is greater than the mode of the distribution, which is the greatest integer in (m + 1) (n + 1)/(l + 2).
Example
Suppose X is a hypergeometric random variable with n = 100, l = 1000, and m = 70. This example evaluates the distribution function at 7.
#include <imsl.h>
#include <stdio.h>
int main()
{
int k = 7;
int l = 1000;
int m = 70;
int n = 100;
float p;
p = imsl_f_hypergeometric_cdf(k,n,m,l);
printf("Pr (x <= 7) = %6.4f\n", p);
}
Output
Pr (x <= 7) = 0.599
Informational Errors
IMSL_LESS_THAN_ZERO | The input argument, k, is less than zero. |
IMSL_K_GREATER_THAN_N | The input argument, k, is greater than the sample size. |
Fatal Errors
IMSL_LOT_SIZE_TOO_SMALL | Lot size must be greater than or equal to n and m. |