How to cite item

Which distributions have the Matsumoto-Yor property?

   
@article{ECP1663,
	author = {Angelo Koudou and Pierre Vallois},
	title = {Which distributions have the Matsumoto-Yor property?},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {16},
	year = {2011},
	keywords = {Gamma distribution; generalized inverse Gaussian distribution; Matsumoto-Yor property; Kummer distribution; Beta distribution.},
	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.},
	pages = {no. 49, 556-566},
	issn = {1083-589X},
	doi = {10.1214/ECP.v16-1663},    
        url = {http://ecp.ejpecp.org/article/view/1663}}