Stochastic Comparison Of Convolutions And Order Statistics Of Generalized Gamma Random Variables

Convolutions and order statistics of independent random variables is an impor-tant topic in many applied areas. There are many applications in reliability theory, electronic engineering, insurance mathematics and quality control and so on. Stochas-tic ordering is an effective research tool in probability theory and mathematical statis-tics. Generalized gamma distribution is a very important distribution in theory and applications, which includes gamma, weibull, exponential, and lognormal as its spe-cial cases. In this thesis, we study the likelihood ratio order of convolutions of two heterogeneous generalized gamma random variables sets wherein they have both the different shape parameters and different scale parameters, then we generalize the re-sult of differing shape parameters to n-dimensional case. We also present that, the ordering properties of the lifetimes of parallel systems with two independent heteroge-neous generalized gamma components. The new results derived here generalize some results known in the literature. Finally, we present the further research direction in the future.