Stochastic comparisons of second-order statistics from dependent and heterogeneous modified proportional (reversed) hazard rates scale models

Abstract

In this paper, we investigate the problem of stochastically comparing the second-order statistics from dependent and heterogeneous samples following modified proportional hazard rates scale (MPHRS) and modified proportional reversed hazard rates scale (MPRHRS) models under Archimedean copula. We built some sufficient conditions for the usual stochastic order whenever the samples have different parameter vectors. Finally, some numerical examples were provided to illustrate the theoretical results.

Keywords

• second-order statistics
• mphrs and mprhrs models
• archimedean copula
• majorization