On characterizations of the gamma and generalized inverse Gaussian distributions

Given two independent non-degenerate positive random variables X and Y, Letac and Wesolowski (Ann. Probab. 28 (2000) 1371) proved that U=( X+ Y) −1 and V= X −1−( X+ Y) −1 are independent if and only if X and Y are generalized inverse Gaussian (GIG) and gamma distributed, respectively. Note that X=(...

Full description

Saved in:
Bibliographic Details
Published in:Statistics & probability letters 2004-10, Vol.69 (4), p.381-388
Main Authors: Chou, Chao-Wei, Huang, Wen-Jang
Format: Article
Language:English
Subjects:
Characterization
Characterization Constancy of regression Gamma distribution Generalized inverse Gaussian distribution Laplace transform
Constancy of regression
Distribution theory
Exact sciences and technology
Gamma distribution
General topics
Generalized inverse Gaussian distribution
Laplace transform
Mathematics
Probability and statistics
Probability theory and stochastic processes
Probability theory on algebraic and topological structures
Sciences and techniques of general use
Statistics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Given two independent non-degenerate positive random variables X and Y, Letac and Wesolowski (Ann. Probab. 28 (2000) 1371) proved that U=( X+ Y) −1 and V= X −1−( X+ Y) −1 are independent if and only if X and Y are generalized inverse Gaussian (GIG) and gamma distributed, respectively. Note that X=( U+ V) −1 and Y= U −1−( U+ V) −1. This interesting transformation between ( X, Y) and ( U, V) preserves a bivariate probability measure which is a product of GIG and gamma distributions. In this work, characterizations of the GIG and gamma distributions through the constancy of regressions of V r on U are considered.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2003.11.021