JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (6): 10-16.doi: 10.6040/j.issn.1671-9352.0.2019.752

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Parameter estimation of linear exponential distribution based on truncated and censored data

SUI Yun-yun1, HU Jiang-shan1, MA Shu-cai2, FU Yun-peng2   

  1. 1. School of Mathematics and Information Science, Weifang University, Weifang 261061, Shandong, China;
    2. School of Economics, Liaoning University, Shenyang 110036, Liaoning, China
  • Published:2020-06-01

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Abstract: The parameter estimation of linear exponential distribution based on truncated and censored data model is studied. The maximum likelihood estimation method and EM algorithm are respectively used to estimate the unknown parameters, and stochastic simulations are carried out. It is found that the parameter estimation obtained by maximum likelihood estimation is similar to that obtained by EM algorithm, but the convergence speed of EM algorithm is faster.

Key words: truncated and censored data, linear exponential distribution, EM algorithm

CLC Number: 

  • O213.9
[1] COHEN A C. Truncated and censored samples[M]. New York: CRC Press, 1991.
[2] BALAKRISHNAN N, COHEN A C. Order statistics and inference: estimation methods[M]. Boston: Academic Press, 1991.
[3] MEEKER W Q, ESCOBAR L A. Statistical methods for reliability data[M]. Hoboken, New Jersey: John Wiley & Sons, 1998.
[4] BALAKRISHNAN N, MITRA D. Some further issues concerning likelihood inference for left truncated and right censored lognormal data[J]. Communications in Statistics-Simulation and Computation, 2013, 43(2):400-416.
[5] WANG Yixin, LIU Peng, ZHOU Yong. Quantile residual lifetime for left-truncated and right-censored data[J]. Science China Mathematics, 2014, 58(6):1217-1234.
[6] TSAI T H, TSAI W Y, CHI Y, et al. Confidence intervals for the ratio of two median residual lifetimes with left-truncated and right-censored data[J]. Biometrics, 2016, 72(1):232-241.
[7] KUNDU D, MITRA D. Bayesian inference of Weibull distribution based on left truncated and right censored data[J]. Computational Statistics and Data Analysis, 2016, 99:38-50.
[8] 何朝兵.右删失左截断数据下离散威布尔分布的参数估计[J]. 郑州大学学报(理学版), 2016, 48(2):18-23. HE Chaobing. Parameter estimations of discrete Weibull distribution with left truncated and right censored data[J]. Journal of Zhengzhou University(Natural Science Edition), 2016, 48(2):18-23.
[9] 胡隽, 曹显兵.基于左截断右删失数据的指数分布参数估计[J]. 统计与决策2016(16):71-73. HU Juan, CAO Xianbing. Estimation of exponential distribution parameters based on left truncated and right censored data[J]. Statistics and Decision, 2016(16):71-73.
[10] SHEN Paosheng, WENG Lining. The Cox-Aalen model for left-truncated and right-censored data[J]. Communications in Statistics-Theory and Methods, 2017, 47(21):5357-5368.
[11] ZHAO Mu, JIANG Hongmei, ZHOU Yong. Estimation of percentile residual life function with left-truncated and right-censored data[J]. Communications in Statistics-Theory and Methods, 2016, 46(2):995-1006.
[12] CHEN C M, SHEN P S, WEI J C, et al. A semiparametric mixture cure survival model for left-truncated and right-censored data[J]. Biometrical Journal, 2017, 59(2):270-290.
[13] CORDEIRO G M, CASTRO M. A new family of generalized distributions[J]. Journal of Statistical Computation and Simulation.2011, 81(7):883-898.
[14] BAIN L J. Statistical analysis of reliability and life-testing models: theory and methods[M]. New York: Marcel Dekker Inc, 1991.
[15] PANDEY A, SINGH A, ZIMMER W J. Bayes estimation of the linear hazard-rate model[J]. IEEE Transactions on Reliability, 1993, 42(4):636-640.
[16] OKASHA H M, AL-SHOMRANI A A. Generalized linear exponential geometric distributions and its applications[J]. Journal of Computational and Applied Mathematics, 2019, 351:198-211.
[17] LANGE K. A gradient algorithm locally equivalent to the EM algorithm[J]. Journal of the Royal Statistical Society(Series B), 1995, 57(2):425-437.
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