Theoretical Statistics and Mathematics Unit, ISI Delhi

On a bivariate lack of memory property under binary associative operation

by B. L. S. Prakasa Rao

A binary operation $\ast$ over real numbers is said to be associative if $(x \ast y) \ast z = x \ast (y \ast z)$
and it is said to be reducible if $x \ast y = x \ast z$ or $y \ast w = z \ast w$ if and only if $z = y$. The
operation $\ast$ is said to have an identity element $e$ if $x \ast e = x$. Roy (2002) introduced a new
definition for bivariate lack of memory property and characterized the bivariate exponential
distribution introduced by Gumbel (1960) under the condition that the each of the conditional
distributions should have the univariate lack of memory property. We generalize this definition
and characterize different classes of bivariate probability distributions under binary associative
operations between random variables.

isid/ms/2003/04 [fulltext]

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