# hygecdf

Hypergeometric cumulative distribution function

## Syntax

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

## Description

`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

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

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.

## Examples

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### Compute Hypergeometric Distribution CDF

Suppose you have a lot of 100 floppy disks and you know that 20 of them are defective. What is the probability of drawing zero to two defective floppies if you select 10 at random?

`p = hygecdf(2,100,20,10)`
```p = 0.6812```