Bernoulli

  • Bernoulli
  • Volume 10, Number 4 (2004), 685-700.

The Matsumoto-Yor property on trees

Hélène Massam and Jacek Wesołowski

Full-text: Open access

Abstract

Viewing the Matsumoto-Yor property as a bivariate property with respect to the simple tree with two vertices and one edge, we extend it to a p-variate property with respect to any tree with p vertices. The converse of the Matsumoto-Yor property, which characterizes the product of a gamma and a generalized inverse Gaussian distribution, is extended to characterize the product of a gamma and p-1 generalized inverse Gaussian distributions. A striking feature of this characterization is that we need the independence of the components of random vectors corresponding only to the leaves of the tree. We illustrate our results with two particular trees: the two-link chain and the three-branch 'daisy'.

Article information

Source
Bernoulli, Volume 10, Number 4 (2004), 685-700.

Dates
First available in Project Euclid: 23 August 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1093265636

Digital Object Identifier
doi:10.3150/bj/1093265636

Mathematical Reviews number (MathSciNet)
MR2076069

Zentralblatt MATH identifier
1055.62012

Keywords
characterization of the product of a gamma and generalized inverse Gaussians gamma independence inverse Gaussian Matsumoto-Yor property tree Wishart

Citation

Massam, Hélène; Wesołowski, Jacek. The Matsumoto-Yor property on trees. Bernoulli 10 (2004), no. 4, 685--700. doi:10.3150/bj/1093265636. https://projecteuclid.org/euclid.bj/1093265636


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References

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