HYPERGEOCDF Function

Evaluates the hypergeometric distribution function.

Usage

result = HYPERGEOCDF(k, n, m, l)

Input Parameters

k—Parameter for which the hypergeometric distribution function is to be evaluated.

n—Sample size. Argument n must be greater than or equal to k.

m—Number of defectives in the lot.

l—Lot size. Parameter l must be greater than or equal to n and m.

Returned Value

result—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.

Input Keywords

Double—If present and nonzero, double precision is used.

Discussion

Function HYPERGEOCDF 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:

 

If k is greater than or equal to i and less than or equal to min(n, m), BINOMIALCDF 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, BINOMIALCDF performs the summation differently, depending on whether or not 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. In this example, the distribution function is evaluated at 7.

p = HYPERGEOCDF(7, 100, 70, 1000)

PM, 'Pr(x <= 7) = ', p, Format = '(a13,f7.4)'

; PV-WAVE prints: Pr(x <= 7) =  0.5995

Informational Errors

STAT_LESS_THAN_ZERO—Input parameter, k, is less than zero.

STAT_K_GREATER_THAN_N—Input parameter, k, is greater than the sample size.

Fatal Errors

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