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Infinitely resizable urn models

Part of: Multivariate analysis Distribution theory - Probability

Published online by Cambridge University Press:  24 November 2025

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

Any margin of the multinomial distribution is multinomially distributed. Retaining this closure property, a family of generalized multinomial distributions is proposed. This family is characterized within multiplicative probability measures, using the Bell polynomial. The retained closure property simplifies marginal properties such as moments. The family can be obtained by conditioning independent infinitely divisible distributions on the total and also by mixing the multinomial distribution with the normalized infinitely divisible distribution. The closure property justifies a stochastic process of the family by Kolmogorov’s extension theorem. Over time, Gibbs partitions of a positive integer appear as the limiting distributions of the family.

Keywords

Bell polynomialconditional compound Poisson distributioninfinite divisibilityoverdispersed multinomial distributionpartition of an integer

MSC classification

Primary: 62H05: Characterization and structure theory
Secondary: 62H17: Contingency tables 60E07: Infinitely divisible distributions; stable distributions

Information

Type
Original Article
Information
Journal of Applied Probability , First View , pp. 1 - 35
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust

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