基于寿命期间数据的极大似然估计

产品的寿命期间是其实际寿命时间与一些未使用时间（比如贮存和运输时间）之和。对寿命期间数据，产品的实际寿命时间未能观测到，本文利用Ｍｏｎｔｅ Ｃａｒｌｏ ＥＭ算法与Ｉｍｐｏｒｔａｎｃｅ Ｓａｍｐｌｉｎｇ方法相结合，给出了产品的寿命时间分布参数以及未使用时间分布参数的极大似然估计，极大似然估计的方差的近似估计也很容易得到，最后还作了随机模拟和实例计算。

Maximun Likelihood Estimate from Life Length Data

The reported life length of a product is not the actural life time, but includes some guarantee times such as storage times and transport times, during which the product is not in use. For life length data, the actural life time is unobserved, the Maximum likelihood Estimates for parameters of life time distribution and guarantee time distribution are presented in this paper, by using the hybrid of Monte Carlo EM algorithm and Importance Sampling method, the variance of estimates can also be obtained conveniently. Our procedure is iustrated by analysing some imulated data and a real example.