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The exact distribution of the maximum, minimum and the range of multinomial/Dirichlet and multivariate hypergeometric frequencies. (English) Zbl 1255.62155

Summary: The exact distribution of the maximum and minimum frequencies of multinomial/Dirichlet and multivariate hypergeometric distributions of \(n\) balls in \(m\) urns is compactly represented as a product of stochastic matrices. This representation does not require equal urn probabilities, is invariant to urn order, and permits rapid calculation of the exact probabilities. The exact distribution of the range is also obtained. These algorithms satisfy a long-standing need for routines to compute exact multinomial/Dirichlet and multivariate hypergeometric maximum, minimum, and range probabilities in statistical computation libraries and software packages.

MSC:

62H10 Multivariate distribution of statistics
62E15 Exact distribution theory in statistics
65C60 Computational problems in statistics (MSC2010)

Software:

AS 145
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Full Text: DOI

References:

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