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Discrete Multivariate Distributions and Generalized Log-Concavity

R. B. Bapat
Sankhyā: The Indian Journal of Statistics, Series A (1961-2002)
Vol. 50, No. 1 (Feb., 1988), pp. 98-110
Published by: Springer on behalf of the Indian Statistical Institute
Stable URL: http://www.jstor.org/stable/25050683
Page Count: 13
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Discrete Multivariate Distributions and Generalized Log-Concavity
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Abstract

For discrete multivariate distributions we introduce a notion called generalized log-concavity and then show that several standard distributions satisfy that property. The multiparameter multinomial density is shown to be generalized log-convave and the proof depends on results from the theory of permanents. The multiparameter negative multinomial density is expressed in terms of permanents and it is shown that the multiparameter negative binomial density is log-concave. The Alexandroff inequality for permanents is used to show that certain sequences associated with the multiparameter multinomial and with order statistics for nonidentically distributed variables are log-concave.

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