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
Publication statusPublished - 1997
Externally publishedYes

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Probability Model
Gaussian distribution
Probability distributions
Cumulants
Generating Function
Inverse Gaussian Distribution
Negative binomial distribution
Binomial distribution
Univariate
Probability Distribution
Limiting
Converge

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Statistics and Probability

Cite this

Multivariate inverse trinomial distribution as a Lagrangian probability model. / Shimizu, Kunio; Nishii, Nobuharu; Minami, Mihoko.

In: Communications in Statistics - Theory and Methods, Vol. 26, No. 7, 1997, p. 1585-1598.

Research output: Contribution to journalArticle

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