Stochastic Comparisons Of Extremal Order Statistics From Exponentiated Gamma Distribution

In this paper,we discuss stochastic comparisons of the smallest and largest or-der statistics with heterogeneous exponentiated gamma components.In the second chapter,we mainly by transforming shape or scale parameters,study the stochas-tic comparisons of extremal order statistics from exponential gamma components in terms of the usual stochastic order,the reversed hazard rate order and the likelihood ratio order.In the third chapter,we discuss the stochastic comparisons of the largest order statistic in terms of reversed hazard rate order and stochastic comparisons of smallest order statistic in terms of the usual stochastic order,under the condition of the shape and scale parameters consisting of a matrix changing to another matrix following the chain majorization order.In the fourth chapter,we study the stochas-tic comparison of the maximum order statistics in terms of reversed hazard rate order when the parameters are restricted in an increasing or a decreasing sequence.