Study on Various Stochastic Comparisons of Order Statistics Arising from General Families of Distributions

Abstract

This thesis addresses the study of various stochastic comparisons of order statistics. The main objective of the thesis is to develop several ordering results between two order statistics according to the usual stochastic order, hazard rate order, reversed hazard rate order, dispersive order, star order, Lorenz order, likelihood ratio order and the ageing faster order. Several sufficient conditions have been established to obtain the comparison results between order statistics, when the random variables are taken from general models, namely, the exponentiated location-scale, MPHRS, MPRHRS and multiple-outlier scale models. These studies comprise two batches of independent or interdependent exponentiated location-scale distributed (MPHRS and MPRHRS distributed, multiple-outlier scale distributed) heterogeneous random variables, where the interdependent observations in sample are modeled by (i) the Archimedean (survival) copula and (ii) the generalized survival copula. Furthermore, several numerical examples/counterexamples are provided to illustrate the effectiveness of the established theoretical results.