# Publications and Preprints

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]