A Multivariate Extension of Inverse Gaussian Distribution Derived from Inverse Relationship

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5 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)2285-2304
Number of pages20
JournalCommunications in Statistics - Theory and Methods
Volume32
Issue number12
DOIs
Publication statusPublished - 2003 Dec
Externally publishedYes

Fingerprint

Inverse Gaussian Distribution
Gaussian distribution
Normal distribution
Multivariate Normal Distribution
Multivariate Distribution
Brownian movement
Infinite Divisibility
Stopping Time
Cumulants
Continuous Distributions
Marginal Distribution
Conditional Distribution
Relationships
Perpendicular
Brownian motion
Higher Order

Keywords

  • Cumulant generating function
  • Inverse relationship
  • Multivariate Brownian motion
  • Multivariate normal distribution

ASJC Scopus subject areas

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

Cite this

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abstract = "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.",
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AB - 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.

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