Theoretical Statistics and Mathematics Unit, ISI Delhi

Characterization of probability distributions via binary associative operation

by Pietro Muliere and 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 $x \ast e = x$. 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.

isid/ms/2002/22 [fulltext]

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