View source for HyperGeometric distribution

[[Category:Distribution Functions]]
[[Category:Discrete distributions]]
[[Category:Bounded distributions]]
[[Category:Unimodal distributions]]
[[Category:Univariate distributions]]
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The hypergeometric distribution describes the number of times an event occurs in a fixed number of trials without replacement -- e.g., the number of red balls in a sample of «Trials» balls drawn without replacement from an urn containing «Size» balls of which «PosEvents» are red. 

<center><code>HyperGeometric( 100, 700, 1000 )</code> &rarr; [[image:hypergeometric_100_700_1000.png]]</center>

== Functions ==
=== <div id="HyperGeometric''>HyperGeometric(trials, posEvents, size)</div> ===
Use this to describe a variable whose outcome has a hyperGeometric distribution.

=== <div id="ProbHyperGeometric''>Prob{{Release||5.1|_}}HyperGeometric(k, trials, posEvents, size)</div> ===
{{Release||5.1|To use, add the [[Distribution Densities Library]] to your model.}}
Returns the probability of outcome «k». It is given by

:<math>p(k) = { {\binom{posEvents}{k} \binom{size-posEvents}{trials-k} } \over \binom{size}{trials} }</math>


=== <div id="CumHyperGeometric''>CumHyperGeometric(k, trials, posEvents, size)</div> ===
{{Release||5.1|To use, add the [[Distribution Densities Library]] to your model.}}
The cumulative probability function for the hyperGeometric distribution. Its value is equal to

:<math>F(k) = \sum_{i=0}^{k} { {\binom{posEvents}{i} \binom{size-posEvents}{trials-i} } \over \binom{size}{trials} }</math>

Use this function when computing the p-Value for a hyperGeometric statistical test.

=== <div id="CumHyperGeometricInv">CumHyperGeometricInv(p, trials, posEvents, size)</div> ===
{{Release||5.1|To use, add the [[Distribution Densities Library]] to your model.}}
The inverse cumulative probability function for the hyperGeometric distribution

=== Parameters ===
;«trials»: The sample size -— e.g., the number of balls drawn from an urn without replacement. Cannot be larger than «Size».
;«posEvents»: The total number of successful events in the population -- e.g, the number of red balls in the urn.
;«size»: The population size -- e.g., the total number of balls in the urn, red and non-red.

=== History ===
* The analytic functions (ProbHyperGeometric, CumHyperGeometric, and CumHyperGeometricInv) were added as built-in functions in [[Analytica 5.2]]. 
* In [[Analytica 5.1]] or earlier, the analytic functions require you to add the [[Distributions Density Library]] to your model.

== See Also ==
* [[Geometric distribution]]{{Release||5.1|
* [[Prob_HyperGeometric]]
* [[Prob_Geometric]]
* [[CumGeometric]]
* [[CumGeometricInv]]}}
* [[Parametric discrete distributions]]
* [[Distribution Densities Library]]