The Exact Distribution of the Maximum, Minimum and the Range of Multinomial/Dirichlet and Multivariate Hypergeometric Frequencies

28 Pages Posted: 29 May 2007 Last revised: 20 Aug 2010

See all articles by Charles J. Corrado

Charles J. Corrado

Deakin University - School of Accounting, Economics & Finance

Date Written: August 19, 2010

Abstract

The exact joint distribution of the maximum and minimum of a multinomial distribution 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 exact probabilities. The exact distribution of the multinomial range is also derived. An application to the September effect in stock returns is presented.

Keywords: Dirichlet multinomial, Multinomial maximum minimum range, Multinomial outliers and inliers, September effect, Stochastic matrix

JEL Classification: C10, C12, C14, C63

Suggested Citation

Corrado, Charles J., The Exact Distribution of the Maximum, Minimum and the Range of Multinomial/Dirichlet and Multivariate Hypergeometric Frequencies (August 19, 2010). Available at SSRN: https://ssrn.com/abstract=989082 or http://dx.doi.org/10.2139/ssrn.989082

Charles J. Corrado (Contact Author)

Deakin University - School of Accounting, Economics & Finance ( email )

221 Burwood Highway
Burwood, Victoria 3215
Australia
61492446214 (Phone)

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