HyperGeometric distribution

Release:	4.6 • 5.0 • 5.1 • 5.2 • 5.3 • 5.4 • 6.0 • 6.1 • 6.2 • 6.3 • 6.4 • 6.5

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 ) →

Functions

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

[math]\displaystyle{ p(k) = { {\binom{posEvents}{k} \binom{size-posEvents}{trials-k} } \over \binom{size}{trials} } }[/math]

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

[math]\displaystyle{ 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.

CumHyperGeometricInv(p, trials, posEvents, size)

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.