HyperGeometric distribution

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4.6  •  5.0  •  5.1  •  5.2

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.

HyperGeometric( 100, 700, 1000 )Hypergeometric 100 700 1000.png


HyperGeometric(trials, posEvents, size)

Use this to describe a variable whose outcome has a hyperGeometric distribution.

ProbHyperGeometric(k, trials, posEvents, size)

Returns the probability of outcome «k». It is given by

$ p(k) = { {\binom{posEvents}{k} \binom{size-posEvents}{trials-k} } \over \binom{size}{trials} } $

Suppose 20 out of 30 balls in a basket are red, and you draw 10 balls at random without replacement. Then the probability of drawing exactly 7 red balls is given by:

ProbHyperGeometric(7, 10, 20, 30) → 0.3096

CumHyperGeometric(k, trials, posEvents, size)

The cumulative probability function for the hyperGeometric distribution. Its value is equal to

$ F(k) = \sum_{i=0}^{k} { {\binom{posEvents}{i} \binom{size-posEvents}{trials-i} } \over \binom{size}{trials} } $

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

CumHyperGeometricInv(p, trials, posEvents, size)

The inverse cumulative probability function for the hyperGeometric distribution


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


See Also


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