Multivariate inverse trinomial distribution as a Lagrangian probability model

Kunio Shimizu, Nobuharu Nishii, Mihoko Minami

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The univariate inverse trinomial distribution is so named because its cumulant generating function (c.g.f.) is the inverse of the c.g.f. of a trinomial distribution. The inverse trinomial distribution, which includes the inverse binomial and negative binomial distributions, is derivable from the Lagrangian expansion. The present paper pertains to the definition of the bivariate and multivariate inverse trinomial distributions through Lagrangian probability distributions. A multivariate inverse binomial distribution, generated by the method of reduction, converges to a multivariate inverse Gaussian distribution as a limiting form.

Original languageEnglish
Pages (from-to)1585-1598
Number of pages14
JournalCommunications in Statistics - Theory and Methods
Volume26
Issue number7
DOIs
Publication statusPublished - 1997 Jan 1
Externally publishedYes

ASJC Scopus subject areas

  • Statistics and Probability

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