逐步Ⅱ型删失数据下Gamma分布的参数推断  

Parameter Inference of Gamma Distribution under Progressive Type-Ⅱ Censored Data

作　　者：王子豪 郭照庄[1] WANG Zihao;GUO Zhaozhuang(School of Liberal Arts and Sciences,North China Institute of Aerospace Engineering,Langfang 065000,China)

机构地区：[1]北华航天工业学院文理学院,河北廊坊065000

出　　处：《新乡学院学报》2025年第3期10-13,共4页Journal of Xinxiang University

基　　金：北华航天工业学院硕士研究生科研创新项目(YKY-2024-62)。

摘　　要：基于逐步Ⅱ型删失方案研究了Gamma分布的参数估计问题,为了克服该删失方案下求解Gamma分布的对数似然函数存在的困难,利用EM算法进行了参数的极大似然估计,利用Bootstrap自助法进行了参数的区间估计,利用Monte-Carlo方法对逐步Ⅱ型删失试验下的参数估计进行模拟。结果表明,随着样本量的增大,参数估计值的平均偏差和均方误差均逐渐减小,区间长度也逐渐变短,利用EM算法对删失数据下Gamma分布进行参数估计是一种有效的方法。The parameter estimation of Gamma distribution is studied based on the stepwise censoring scheme.In order to overcome the difficulty of solving the log-likelihood function of Gamma distribution under this censoring scheme,the EM algorithm is used to estimate the maximum likelihood of the parameters,and the Bootstrap method is used to estimate the interval of the parameters.The Monte-Carlo method is used to simulate the parameter estimation under the progressive type Ⅱ censoring test.The results show that as the sample size increases,the average deviation and mean square error of the parameter estimates gradually decreases,and the interval length of the parameter estimates gradually becomes shorter.The proposed EM algorithm is effective for parameter estimation of the Gamma distribution of censored data.

关 键 词：GAMMA分布 逐步Ⅱ型删失 EM算法 Bootstrap区间估计 

分 类 号：O213.2[理学—概率论与数理统计]