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A discrete multivariate distribution resulting from the law of small numbers

Published online by Cambridge University Press:  14 July 2016

Nobuaki Hoshino*
Affiliation:
Kanazawa University
*
Postal address: Faculty of Economics, Kanazawa University, Kakuma-machi, Kanazawa-shi, Ishikawa, 920-1192, Japan. Email address: [email protected]
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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.

Type
Research Article
Copyright
© Applied Probability Trust 2006 

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