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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2015, Vol. 30 Issue (2): 127-138    DOI:
    
Parameter estimation of Weibull distribution with multiple change points 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 the missing data of the life variable, the complete-data likelihood function of Weibull distribution with multiple change points for truncated and censored data is obtained. The full conditional distributions of change-point positions, shape parameters, and scale parameters are studied. Gibbs samples of the parameters are obtaines by MCMC method of Gibbs sampling together with Metropolis-Hastings algorithm, and the means of Gibbs samples are taken as Bayesian estimations of the parameters. 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： complete-data likelihood function      full conditional distribution      MCMC method      Gibbs sampling      Metropolis-Hastings algorithm     
Received: 14 December 2014      Published: 05 June 2018
CLC:  O213.2  
  O212.8  
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HE Chao-bing. Parameter estimation of Weibull distribution with multiple change points for truncated and censored data. Applied Mathematics A Journal of Chinese Universities, 2015, 30(2): 127-138.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2015/V30/I2/127


删失截断情形下Weibull分布多变点模型的参数估计

通过添加缺失的寿命变量数据, 得到了删失截断情形下Weibull分布多变点模型的完全数据似然函数, 研究了变点位置参数和形状参数以及尺度参数的满条件分布. 利用Gibbs抽样与Metropolis-Hastings算法相结合的MCMC方法得到了参数的Gibbs样本, 把Gibbs样本的均值作为各参数的Bayes 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估计的精度都较高.

关键词： 完全数据似然函数,  满条件分布,  MCMC方法,  Gibbs抽样,  Metropolis-Hastings算法 
[1] HE Chao-bing. Bayesian parameter estimation of failure rate model with a change point for truncated and censored data[J]. Applied Mathematics A Journal of Chinese Universities, 2016, 31(4): 413-427.
[2] CHENG Di, ZHANG Shi-bin. Bayesian inference for dynamic heterogeneity stochastic frontier model[J]. Applied Mathematics A Journal of Chinese Universities, 2016, 31(2): 127-135.