# Negative hypergeometric distribution

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In probability theory and statistics, the **hypergeometric distribution** is a discrete probability distribution that describes the probability of successes in draws *without* replacement from a finite population of size containing a maximum of successes. This is in contrast to the binomial distribution, which describes the probability of successes in draws *with* replacement.

## Definition

The **negative hypergeometric distribution** describes the probability of the number of elements taken without replacement from a finite population whose elements can be classified into two mutually exclusive categories like Pass/Fail, Male/Female or Employed/Unemployed that stops when a fixed number of elements of certain class have been taken. As random selections are made from the population, each subsequent draw decreases the population causing the probability of success to change with each draw.

## References

- Skala, M. (2011) "Hypergeometric tail inequalities: ending the insanity", unpublished note

## External links

- The Hypergeometric Distribution and Binomial Approximation to a Hypergeometric Random Variable by Chris Boucher, Wolfram Demonstrations Project.
- Weisstein, Eric W., "Hypergeometric Distribution",
*MathWorld*.

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