Multivariate inverse Gaussian distribution as a limit of multivariate waiting time distributions

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Abstract

Multivariate inverse Gaussian distribution proposed by Minami [2003. A multivariate extension of inverse Gaussian distribution derived from inverse relationship. Commun. Statist. Theory Methods 32(12), 2285-2304] was derived through multivariate inverse relationship with multivariate Gaussian distributions and characterized as the distribution of the location at a certain stopping time of a multivariate Brownian motion. In this paper, we show that the multivariate inverse Gaussian distribution is also a limiting distribution of multivariate Lagrange distributions, which is a family of waiting time distributions, under certain conditions.

Original languageEnglish
Pages (from-to)3626-3633
Number of pages8
JournalJournal of Statistical Planning and Inference
Volume137
Issue number11
DOIs
Publication statusPublished - 2007 Nov 1

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Keywords

  • Branching process
  • Cumulants
  • Inverse relationship
  • Lagrange expansion
  • Multivariate Lagrange distributions

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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