A Multivariate Extension of Inverse Gaussian Distribution Derived from Inverse Relationship

研究成果: Article査読

6 被引用数 (Scopus)

抄録

We propose a new multivariate extension of the inverse Gaussian distribution derived from a certain multivariate inverse relationship. First we define a multivariate extension of the inverse relationship between two sets of multivariate distributions, then define a reduced inverse relationship between two multivariate distributions. We derive the multivariate continuous distribution that has the reduced multivariate inverse relationship with a multivariate normal distribution and call it a multivariate inverse Gaussian distribution. This distribution is also characterized as the distribution of the location of a multivariate Brownian motion at some stopping time. The marginal distribution in one direction is the inverse Gaussian distribution, and the conditional distribution in the space perpendicular to this direction is a multivariate normal distribution. Mean, variance, and higher order cumulants are derived from the multivariate inverse relationship with a multivariate normal distribution. Other properties such as reproductivity and infinite divisibility are also given.

本文言語English
ページ(範囲)2285-2304
ページ数20
ジャーナルCommunications in Statistics - Theory and Methods
32
12
DOI
出版ステータスPublished - 2003 12月 1
外部発表はい

ASJC Scopus subject areas

  • 統計学および確率

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