Some Stochastic Comparison Properties Of Dependent Extremum

This article mainly studies the stochastic comparison properties of samples ex-tremum in dependent cases.Firstly,the n-dimensional independent samples with ex-ponential distribution are considered.We obtain the stochastic comparison properties of samples maximum order statistics in the sense of likelihood ratio order,hazard rate order and reverse hazard rate order.At the same time,these results are applied to the proportional hazard rate model and the Weibull distribution model.Secondly,we con-sider two homogeneous samples following the Clayton survival copula distribution.We get some properties of the failure rate functions of samples extremum.Several depen-dent properties and the comparison properties of two samples residual life are obtained.These are supplements of some results in existing literatures.Finally,we mainly dis-cuss the n-dimensional heterogeneous samples associated with an Archimedean survival copula.We obtain the stochastic comparison properties of the samples order statistics(3_1:9),(3_1:9+1),(3_2:9)in the sense of hazard rate order and reverse hazard rate order.In addition,the n-dimensional heterogeneous samples associated with an Archimedean copula are considered.We get the stochastic comparison properties of the samples maximum order statistics(3₉:9)),(3₉+1:9)+1)in the sense of hazard rate order.These are supplements of some results in existing literatures.