The Random Properties Of The Maximum And Minimum Order Statistics Of Dependence Samples

In this paper,we discuss the random properties of the maximum and minimum order statistics of samples in the case of sample independence and sample dependence.Firstly,we discuss stochastic comparison properties of the maximum order statistics with independent exponential sample in the sense of the likelihood ratio order.We also discuss PHR and independent samples of weibull distribution model,respectively.We obtained the likelihood ratio order properties of their maximum order statistics.Secondly,in the dependent sample situation,when the two samples obey Marshall-Olkin exponential distribution,we study stochastic comparison properties of the largest order statistics in the sense of likelihood ratio order.We gain two sufficient conditions which make the lemma 4.1.1 valid in the sense of the likelihood ratio order(theorem 4.1.2 and theorem 4.1.8).Some stochastic comparison properties of the largest order statistics which samples obey generalized Marshall-Olkin distribution are obtained.Finally,we study the hazard rate properties of minimum order statistics with two samples obey FGM copulas distribution.