HYPDF
This function evaluates the hypergeometric cumulative distribution function.
Function Return Value
HYPDF — Function value, the probability that a hypergeometric random variable takes a value less than or equal to K. (Output)
HYPDF is 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.
See Comment 1.
Required Arguments
K — Argument for which the hypergeometric cumulative distribution function is to be evaluated. (Input)
N — Sample size. (Input)
N must be greater than zero and greater than or equal to K.
M — Number of defectives in the lot. (Input)
L — Lot size. (Input)
L must be greater than or equal to N and M.
FORTRAN 90 Interface
Generic: HYPDF (K, N, M, L)
Specific: The specific interface names are S_HYPDF and D_HYPDF.
FORTRAN 77 Interface
Single: HYPDF (K, N, M, L)
Double: The double precision name is DHYPDF.
Description
The function HYPDF evaluates the cumulative 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), HYPDF sums the terms in this expression for j going from i up to k. Otherwise, HYPDF returns 0 or 1, as appropriate. So, as to avoid rounding in the accumulation, HYPDF 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).
Comments
1. If the generic version of this function is used, the immediate result must be stored in a variable before use in an expression. For example:
X = HYPDF(K, N, M, L)
Y = SQRT(X)
must be used rather than
Y = SQRT(HYPDF(K, N, M, L))
If this is too much of a restriction on the programmer, then the specific name can be used without this restriction.
2. Informational errors
Type | Code | Description |
|---|
1 | 5 | The input argument, K, is less than zero. |
1 | 6 | The input argument, K, is greater than the sample size. |
Example
Suppose X is a hypergeometric random variable with n = 100, l = 1000, and m = 70. In this example, we evaluate the distribution function at 7.
USE UMACH_INT
USE HYPDF_INT
IMPLICIT NONE
INTEGER K, L, M, N, NOUT
REAL DF
!
CALL UMACH (2, NOUT)
K = 7
N = 100
L = 1000
M = 70
DF = HYPDF(K,N,M,L)
WRITE (NOUT,99999) DF
99999 FORMAT (' The probability that X is less than or equal to 7 is ' &
, F6.4)
END
Output
The probability that X is less than or equal to 7 is 0.5995
