Title: A Multivariate Extension of Inverse Gaussian Distribution Derived from Inverse Relationship
Abstract: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 ...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. Keywords: Inverse relationshipCumulant generating functionMultivariate Brownian motionMultivariate normal distribution Acknowledgments The author would like to thank the referee and associate editor for their helpful comments and suggestions.Read More
Publication Year: 2003
Publication Date: 2003-01-12
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 12
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