Cdf.Hypergeometric Method

Evaluates the hypergeometric cumulative probability distribution function.

public static double Hypergeometric(
   int k,
   int sampleSize,
   int defectivesInLot,
   int lotSize
);

Parameters

k: An int specifying the argument at which the function is to be evaluated.
sampleSize: An int specifying the sample size, n.
defectivesInLot: An int specifying the number of defectives in the lot, m.
lotSize: An int specifying the lot size, l.

Return Value

A double specifying the probability that a hypergeometric random variable takes a value less than or equal to k.

Remarks

Method Hypergeometric 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

$\Pr \left( {X = j} \right) = \frac{{\left( {_j^m } \right)\left( {_{n - j}^{l - m} } \right)}}{{\left( {_n^l } \right)}}{\rm{for }}\,\,j = i,\;i + 1,\,\,i + 2,\; \ldots ,\;\min \left( {n,m} \right)$

where $i = {\rm max}(0, n - l + m)$ .

If k is greater than or equal to i and less than or equal to $\min (n, m)$ , Hypergeometric sums the terms in this expression for j going from i up to k. Otherwise, 0 or 1 is returned, as appropriate. So, as to avoid rounding in the accumulation, Hypergeometric 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 .

Cdf.Hypergeometric Method

Parameters

Return Value

Remarks

See Also