الفهرس 
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Abstract
This thesis presents contributed results to the area or characterization of commonly used probability distribution. The considered distributions have several applications in operations research (particularly in queuing theory and the replacement policies) as well as the theory of probability and statistical
inference. Engineers can use the new results of this thesis to identify the underlying distributions by easily estimating the mean inactivity times frorn their data as well as estimating the reversed failure rate and then checking the proved equalities to obtain the distribution that their data is. This is much easier for an engineer instead of trying to use goodness of fit techniques andlor density estimation. Using conditional expectations, we present results that lead to the characterization of several distributions. The characterizations cover both discrete (the Poisson, the binomial and the negative binomial) distributions and• continuous (gamma
and four-parameter beta) distributions. Mixtures of geometric distribution are also considered. Finally characterization of Harris distribution and relations to the negative binomial distribution are identified. Applications to simulation, operations research, stochastic modeling and goodness-of-fit tests arc discussed. Topics and open points for future research are also included.