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1 results

  • A discrete multivariate distribution resulting from the law of small numbers

  • Part of
  • Nobuaki Hoshino
  • Journal:
    Journal of Applied Probability / Volume 43 / Issue 3 / September 2006
    Published online by Cambridge University Press:
    14 July 2016, pp. 852-866
    Print publication:
    September 2006
    • Article
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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.