Stochastic Order And Application Of Extreme Statistics From Population Following MPHR And MPRHR Models

Order statistics is an important concept in statistics,which has been widely used in reliability theory,auction theory,actuarial theory and stochastic operations research.As the most important order statistics,extreme statistic has been widely concerned by academia and industry in recent years,and a series of fruitful research achievements have been obtained.In this thesis,we carry out stochastic comparison of extreme statistics with populations subject to MPHR and MPRHR models.Stochastic comparison of extreme statistics(i.e.,minimum and maximum order statistics)under the usual stochastic order,hazard rate order and reversed hazard rate order are obtained for the modified proportional hazard rate(MPHR)and modified proportional reversed hazard rate(MPRHR)random samples by means of stochastic order.Based on the dependent structure of Archimedean Copula,the usual stochastic order,hazard rate order and reversed hazard rate order among extreme order statistics are bulit by the change of parameters,and generalize the some results of Fang et al.^[1]and Balakrishnan et al.^[2]Meanwhile,some numerical examples are given to illurstrate the reliability of the theoretical results and give some applications in practice.