IMSL_HYPERGEOCDF

Syntax | Return Value | Arguments | Keywords | Discussion | Example | Errors | Version History

The IMSL_HYPERGEOCDF function evaluates the hypergeometric distribution function.

Note
This routine requires an IDL Advanced Math and Stats license. For more information, contact your ITT Visual Information Solutions sales or technical support representative.

Syntax

Result = IMSL_HYPERGEOCDF(k, n, m, l [, /DOUBLE] )

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.

Arguments

k

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

l

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

m

Number of defectives in the lot.

n

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

Keywords

DOUBLE

If present and nonzero, double precision is used.

Discussion

The IMSL_HYPERGEOCDF function 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_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, IMSL_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 = IMSL_HYPERGEOCDF(7, 100, 70, 1000) 
PM, 'Pr(x <= 7) = ', p, FORMAT = '(a13,f7.4)' 
 
Pr(x <= 7) =  0.5995 

Errors

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.

Version History