Publications and Preprints

A binary operation $*$ over real numbers is said to be associative if $(x*y)*z$=$x*(y*z)$ and it 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 $x*\tilde{e} = x$. We study different classes of lifetime probability distributions under binary associative operations between random variables.