BUILT-IN MATHEMATICA SYMBOL

MultivariateHypergeometricDistribution

represents a multivariate hypergeometric distribution with n draws without replacement from a collection containing

objects of type i.

MORE INFORMATION

The probability for a vector of non-negative integers , , ..., in a multinomial distribution is proportional to given that .

The numbers can be any non-negative integers and n any positive integer less than or equal to .

The number of trials n can be any positive integer and any non-negative integer.

MultivariateHypergeometricDistribution can be used with such functions as Mean, CDF, and RandomVariate.

EXAMPLES

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Basic Examples (4)

Probability density function:

Cumulative distribution function:

Mean and variance:

Covariance:

Probability density function:

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Cumulative distribution function:

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Mean and variance:

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Covariance:

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Scope (7)

Generate a set of pseudorandom numbers that are multivariate hypergeometric distributed:

Compare its histogram to the PDF:

Distribution parameters estimation:

Estimate the distribution parameters from sample data:

Goodness-of-fit test:

Skewness:

The distribution becomes symmetric with an equal number of objects:

Kurtosis:

In the limit it behaves like a binormal distribution:

Correlation:

Hazard function:

Marginals do not simplify to known distributions:

Applications (1)

An urn contains 12 red balls, 23 blue balls, and 9 green balls. Find the distribution of a sample of 5 balls drawn without replacement:

Find the probability of exactly 2 red balls and 3 green balls in the sample:

Find the average number of balls of each color in a sample:

Simulate the composition of 30 samples:

Visualize the samples:

Properties & Relations (2)

Relationships to other distributions:

Bivariate hypergeometric distribution is equivalent to HypergeometricDistribution: