On stochastic comparisons of maximum order statistics from the location-scale family of distributions

Abstract

We consider the location-scale family of distributions, which contains many standard lifetime distributions. We give conditions under which the largest order statistic of a set of random variables with different/the same location as well as different/the same scale parameters dominates that of another set of random variables with respect to various stochastic orders. Along with general results, we consider important special cases, namely, the Feller–Pareto, generalized Pareto, Burr, exponentiated Weibull, Power generalized Weibull, generalized gamma, Half-normal and Fréchet distributions.