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Hypergeometric cumulative distribution function

`hygecdf(x,M,K,N)`

hygecdf(x,M,K,N,'upper')

`hygecdf(x,M,K,N)`

computes
the hypergeometric cdf at each of the values in `x`

using
the corresponding size of the population, `M`

, number
of items with the desired characteristic in the population, `K`

,
and number of samples drawn, `N`

. Vector or matrix
inputs for `x`

, `M`

, `K`

,
and `N`

must all have the same size. A scalar input
is expanded to a constant matrix with the same dimensions as the other
inputs.

`hygecdf(x,M,K,N,'upper')`

returns the complement
of the hypergeometric cdf at each value in `x`

, using
an algorithm that more accurately computes the extreme upper tail
probabilities.

The hypergeometric cdf is

$$p=F(x|M,K,N)={\displaystyle \sum _{i=0}^{x}\frac{\left(\begin{array}{c}K\\ i\end{array}\right)\left(\begin{array}{c}M-K\\ N-i\end{array}\right)}{\left(\begin{array}{c}M\\ N\end{array}\right)}}$$

The result, *p*, is the probability of drawing
up to *x* of a possible *K* items
in *N* drawings without replacement from a group
of *M* objects.