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A discrete multivariate distribution resulting from the law of small numbers

Part of: Distribution theory - Probability Distribution theory Applications

Published online by Cambridge University Press:  14 July 2016

Nobuaki Hoshino
Nobuaki Hoshino*
Affiliation:
Kanazawa University
*
∗Postal address: Faculty of Economics, Kanazawa University, Kakuma-machi, Kanazawa-shi, Ishikawa, 920-1192, Japan. Email address: hoshino@kenroku.kanazawa-u.ac.jp
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Abstract

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In the present article we derive a new discrete multivariate distribution using a limiting argument that is essentially the same as the law of small numbers. The distribution derived belongs to an exponential family, and randomly partitions positive integers. The facts shown about the distribution are useful in many fields of application involved with count data. The derivation parallels that of the Ewens distribution from the gamma distribution, and the new distribution is produced from the inverse Gaussian distribution. The method employed is regarded as the discretization of an infinitely divisible distribution over nonnegative real numbers.

Keywords

Conditional inverse Gaussian-Poisson distributionextended negative binomial modelfrequencies of frequenciesinfinite divisibilityrandom clusteringspecies abundance

MSC classification

Primary: 62E10: Characterization and structure theory 60E07: Infinitely divisible distributions; stable distributions
Secondary: 62P99: None of the above, but in this section
Type
Research Article
Information
Journal of Applied Probability , Volume 43 , Issue 3 , September 2006 , pp. 852 - 866
Copyright
© Applied Probability Trust 2006 

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