复杂删失模型下指数威布尔分布的参数估计

Parameter Estimation of Exponential Weibull Distribution under Complex Censored Model

摘要: 针对服从指数威布尔分布的逐步II型删失模型，分别用极大似然方法和贝叶斯方法对指数威布尔分布的两个未知参数进行了估计。其中，使用Newton-Raphson方法获得了参数的极大似然估计值，使用Metropolis-Hastings算法获得了参数的贝叶斯估计值。通过蒙特卡洛方法对这两种估计方法的性能进行了评估，结果表明两种方法的估计效果都很好，且贝叶斯估计优于极大似然估计。最后，通过分析一组实际数据进一步证明了本文所提估计方法的精确性。

Abstract: The maximum likelihood method and Bayesian method are used to estimate the two unknown parameters of the exponential Weibull distribution for the progressively type II censoring model that follows the exponential Weibull distribution. The maximum likelihood estimation of param-eters is obtained by Newton-Raphson method, and the Bayesian estimation of parameters is ob-tained by Metropolis-Hastings algorithm. The performance of these two estimation methods is evaluated by Monte Carlo method. The results show that the estimation effects of the two methods are very good, and Bayesian estimation is better than maximum likelihood estimation. Finally, the accuracy of the proposed estimation method is further proved by analyzing a group of actual data.