Some Researches On Proportional Mean Residual Life Model

In this paper,the aging properties and stochastic orders for dynamic proportional mean residual life model are investigated,and the large-sample theory of MLE of parameter for proportional mean residual life model with incomplete information is discussed.First,we study some closure properties of aging properties and stochastic comparisons for two random variables satisfied dynamic proportional mean residual life model.Distinguished from literatures based on survival function or hazard rate function,Our research is based on the mean residual life function.In this paper,we present the sufficient conditions which certify the same aging properties and Stochastic orders of two random variables satis-fied dynamic proportional mean residual life model,and we provide the illustrations which prove that conditions are necessary.Second,we discuss the MLE of parameter based on the data with random censorship and incomplete information. In survival analysis the proportional mean residual life model is a significant regression model and the right censoring data with incomplete information is a common data type. The research on proportional mean residual life model randomly censored with incomplete information is very meaningful.The proportional mean residual life model based on the data with random right censorship and incomplete information isn’t discussed in the existent literatures. Under suitable assumptions, we obtain the existence,consistency, asymptotic normality.Finally,the law of iterated logarithm,the Chung type law of iterated logarithm and the moderate deviation of MLE of unknown parameters under the model are obtained.