CIRJE-F-361. Hoshino, Nobuaki, "On a limiting quasi-multinomial distribution", August 2005.

A random clustering distribution is useful for modeling count data. The present article derives a new distribution of this type from the Lagrangian Poisson distribution, based on the result that any infinitely divisible distribution over nonnegative integers produces a random clustering distribution through conditioning and a limiting argument that is equivalent to the law of small numbers. The resulting distribution is shown to be tractable. Its application is also presented.