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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2016, Vol. 31 Issue (4): 413-427    DOI:
    
Bayesian parameter estimation of failure rate model with a change point for truncated and censored data
HE Chao-bing
School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, China
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Abstract  By filling in some missing data of the life variable, the relatively simple likelihood function of failure rate model with a change point for truncated and censored data is obtained. The probability distribution and random sampling method of the missing data variable fillled in are discussed. All the unknown parameters are iterated by MCEM algorithm. The parameters are sampled from their full conditional distributions by Gibbs sampler together with Metropolis-Hastings algorithm, and are estimated based on Gibbs sample. The implementation steps of MCMC method are introduced in detail. The random simulation test results show that Bayesian estimations of the parameters are fairly accurate.

Key words： failure rate      exponential distribution      EM algorithm      Gibbs sampling      Metropolis-Hastings algorithm      truncated normal distribution     
Received: 19 January 2016      Published: 16 May 2018
CLC:  O213.2  
  O212.8  
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HE Chao-bing. Bayesian parameter estimation of failure rate model with a change point for truncated and censored data. Applied Mathematics A Journal of Chinese Universities, 2016, 31(4): 413-427.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2016/V31/I4/413


删失截断情形下失效率变点模型的Bayes参数估计

通过添加部分缺失寿命变量数据, 得到了删失截断情形下失效率变点模型相对简单的似然函数. 讨论了所添加缺失数据变量的概率分布和随机抽样方法. 利用Monte Carlo EM算法对未知参数进行了迭代. 结合Metropolis-Hastings算法对参数的满条件分布进行了Gibbs抽样, 基于Gibbs样本对参数进行估计, 详细介绍了MCMC方法的实施步骤. 随机模拟试验的结果表明各参数Bayes估计的精度较高.

关键词： 失效率,  指数分布,  EM算法,  Gibbs抽样,  Metropolis-Hastings算法,  截断正态分布 
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