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Which distributions have the Matsumoto-Yor property?


 
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1. Title Title of document Which distributions have the Matsumoto-Yor property?
 
2. Creator Author's name, affiliation, country Angelo Efoevi Koudou; Institut Elie Cartan, Nancy, France
 
2. Creator Author's name, affiliation, country Pierre Vallois; Institut Elie Cartan, Nancy, France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Gamma distribution; generalized inverse Gaussian distribution; Matsumoto-Yor property; Kummer distribution; Beta distribution.
 
3. Subject Subject classification 60E05; 62E10
 
4. Description Abstract For four types of functions $ξ : ]0,∞[→ ]0,∞[$, we characterize the law of two independent and positive r.v.'s $X$ and $Y$ such that $U:=ξ(X+Y)$ and $V:=ξ(X)-ξ(X+Y)$ are independent. The case $ξ(x)=1/x$ has been treated by Letac and Wesolowski (2000). As for the three other cases, under the weak assumption that $X$ and $Y$ have density functions whose logarithm is locally integrable, we prove that the distribution of $(X,Y)$ is unique. This leads to Kummer, gamma and beta distributions. This improves the result obtained in [1] where more regularity was required from the densities.
 
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7. Date (YYYY-MM-DD) 2011-09-29
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1663
 
10. Identifier Digital Object Identifier 10.1214/ECP.v16-1663
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 16
 
12. Language English=en
 
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