Publications and Preprints

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 $x \ast e = x$. We characterize different classes of probability distributions under binary operations between random variables. Further more we characterize distributions with the almost lack of memory property or with strong Markov property or with periodic failure rate under such a binary operation extending the results on exponential distributions under addition operation as binary operation.