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

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.