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The Matsumoto–Yor independence property for GIG and Gamma laws, revisited

Published online by Cambridge University Press:  02 August 2002

JACEK WESOŁOWSKI
JACEK WESOŁOWSKI
Affiliation:
Wydział Matematyki i Nauk Informacyjnych, Politechnika Warszawska, Warszawa, Poland. e-mail: wesolo@alpha.mini.pw.edu.pl
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Abstract

Matsumoto and Yor have recently discovered an interesting invariance property of a product of the generalized inverse Gaussian and gamma distributions. In this paper we obtain: (1) a complete regression version of its converse; (2) a converse to the matrix variate Matsumoto–Yor property which extends an earlier result. Of independent interest is a functional equation for matrix valued functions, which has been solved in the course of investigation of the second problem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 133 , Issue 1 , July 2002 , pp. 153 - 161
Copyright
2002 Cambridge Philosophical Society

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