HAL : hal-00536648, version 1

Fiche détaillée

Récupérer au format BibTeX - EndNote - TEI - RefWorks -

Independence properties of the Matsumoto-Yor type

Angelo Efoévi Koudou 1, Pierre Vallois 1, 2

(2010)

We define Letac-Wesolowski-Matsumoto-Yor (LWMY) functions as decreasing functions from (0,\infty) onto (0,\infty) with the following property: there exist independent, positive random variables $X$ and $Y$ such that the variables $f(X + Y)$ and $f(X) − f(X + Y)$ are independent. We prove that, under additional assumptions, there are essentially four such functions. The first one is $f(x) = \frac{1}{x}$. In this case, referred to in the literature as the Matsumoto-Yor property, the law of $X$ is generalized inverse Gaussian while $Y$ is gamma-distributed. In the three other cases, the associated densities are provided. As a consequence, we obtain a new relation of convolution involving gamma distributions and Kummer distributions of type 2.

1 :	Institut Elie Cartan Nancy (IECN)
	CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
2 :	BIGS (INRIA Lorraine / IECN)
	INRIA – CNRS : UMR7502

Domaine

:

Mathématiques/Probabilités Mathématiques/Statistiques Statistiques/Théorie

Mots Clés : Gamma distribution – Generalized inverse Gaussian distribution – Matsumoto- Yor property – Kummer distribution.

hal-00536648, version 1

http://hal.archives-ouvertes.fr/hal-00536648

oai:hal.archives-ouvertes.fr:hal-00536648

Contributeur : Pierre Vallois <>

Soumis le : Mardi 16 Novembre 2010, 16:13:32

Dernière modification le : Lundi 21 Novembre 2011, 18:14:02