δ冲击模型中截尾数据的统计推断

本文研究了δ-冲击模型中参数δ的统计推断问题，该模型具有参数为λ的Poisson冲击，系统在当两个连续的冲击时间间隔小于δ时失效，失效的时间记为T．首先，我们给出了在δ小于平均冲击间隔时间(即1／λ)的情况下，失效时间T的密度函数的性质；然后我们给出了截尾数据的损失信息补偿的方法；借助Class-K方法，给出了δ的无偏、一致估计以和区间估计．最后，由Edgeworth展开和Boostrap方法，我们得到了δ的精确度更高的区间估计．

Statistical Inference on δ Shock Model with Censored Data

In this paper we study some statistical problems of the parameter δ of the δ-shock model associated with a Poisson process with intensity λ under censoring data. Where the system fails when the length of an interval of two successive shocks falls below δ, and the failure time is denoted by T. Firstly we analyze the shape of the density function of T on condition that δ is less than the mean time 1/λ of the Poisson shock. Next open window method is used to compensate some of the information which is lost due to type I censoring. Then we take advantage of Class-K method so as to obtain an unbiased and consistent estimator of E(T), simultaneously to get both a point estimator and an approximate confidence interval of δ. In the end a more accurate confidence interval of δ is given by means of Edgeworth expansion and Boostrap.