MRL ordering of largest order statistics from heterogeneous scale variables

For comparing largest order statistics from independent heterogeneous non-negative scale variables in the mean residual life order, a new framework is introduced here. This framework can be viewed as a generalization of the well-known multiple-outlier scale model, and it additionally includes the situation in which all the random variables are heterogeneous. We also find some sufficient conditions for comparing the largest order statistics, one with complete heterogeneous scale parameters and another with homogeneous scale parameters, in the mean residual life order. As examples of the obtained results, generalized gamma, generalized beta of the second kind, power-generalized Weibull, and half-normal distributions are all presented. The findings of this work generalize and also reinforce some of the existing results in this direction.