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# MultivariateHypergeometricDistribution

 MultivariateHypergeometricDistribution represents a multivariate hypergeometric distribution with n draws without replacement from a collection containing objects of type i.
• 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.
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:
Relationships to other distributions:
Bivariate hypergeometric distribution is equivalent to HypergeometricDistribution:
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