## Probability models characterized by generalized reversed lack of memory property

##### Authors
Gopalakrishnan, Asha
John, Rejeesh C.
##### Description
A binary operator * over real numbers is said to be associative if $(x*y)*z=x*(y*z)$ and is said to be reducible if $x*y=x*z$ or $y*w=z*w$ if and only if $z=y$. The operation is said to have an identity element $\tilde{e}$ if $x*\tilde{e}=x$. In this paper a characterization of a subclass of the reversed generalized Pareto distribution (Castillo and Hadi (1995)) in terms of the reversed lack of memory property (Asha and Rejeesh (2007)) is generalized using this binary operation and probability distributions are characterized using the same. This idea is further generalized to the bivariate case.
Comment: Submitted to the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)
##### Keywords
Mathematics - Statistics Theory