JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (7): 46-52.doi: 10.6040/j.issn.1671-9352.0.2020.390

Previous Articles    

Bayesian inference of Poisson distribution based on left truncated and right censored data

HU Jiang-shan1, SUI Yun-yun1, 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:2021-07-19

PDF (PC)

239

Abstract: The Bayesian inference of Poisson distribution in left truncated and right censored data is studied. The maximum likelihood estimation method and Bayesian estimation are respectively used to estimate the unknown parameters. Meanwhile the corresponding confidence intervals are given, and stochastic simulations are carried out. It is found that in the case of small sample, the accuracy of Bayesian estimator is higher than that of maximum likelihood estimator, while in the case of large sample, the accuracy of these two estimators is not much different. In terms of confidence interval, the confidence interval of the highest posterior probability density constructed is indeed more effective than the traditional confidence interval, no matter it is a small sample or a large sample.

Key words: Bayesian estimation, prior distribution, confidence interval

CLC Number: 

  • O213
[1] SHEN P S, WENG L N. The Cox-Aalen model for left-truncated and right-censored data[J]. Communications in Statistics: Theory and Methods, 2018, 47(21): 5357-5368.
[2] ZHAO M, JIANG H M, ZHOU Y. Estimation of percentile residual life function with left-truncated and right-censored data[J]. Communications in Statistics: Theory and Methods, 2017, 46(2): 995-1006.
[3] TSAI T H, TSAI W Y, CHI Y C, 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.
[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, 2014, 43(2): 400-416.
[5] 何朝兵,柴士改,刘华文. 截断删失数据下泊松分布参数的点估计[J].华南师范大学学报(自然科学版), 2015, 47(2): 141-145. HE Chaobing, CHAI Shigai, LIU Huawen. Point estimation of parameter of Poisson distribution for truncated and censored data [J]. Journal of South China Normal University(Natural Science Edition), 2015, 47(2): 141-145.
[6] 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.
[7] KUNDU D, MITRA D. Bayesian inference of Weibull distribution based on left truncated and right censored data[J]. Computational Statistics & Data Analysis, 2016, 99: 38-50.
[8] SUNITA K. Poisson distribution in real life [J]. International Journal of Engineering, Science and Mathematics, 2018, 7(4): 284-290.
[9] PUDOVKIN A I, BORNMANN L. Approximation of citation distributions to the Poisson distribution[J]. COLLNET Journal of Scientometrics and Information Management, 2018, 12(1): 49-53.
[10] GRAMMER R T. The Poisson distribution in biology instruction[J]. The American Biology Teacher, 2017, 79(1): 10-13.
[11] RODRIGUES G C, LOUZADA F, RAMOS P L. Poisson-exponential distribution: different methods of estimation[J]. Journal of Applied Statistics, 2018, 45(1): 128-144.
[12] BUDGETT S, PFANNKUCH M. Modeling and linking the Poisson and exponential distributions[J]. ZDM, 2018, 50(7): 1281-1294.
[13] 李中恢. 威布尔分布参数的最高后验概率密度区间估计算法[J]. 浙江大学学报(理学版), 2010, 37(5): 515-518. LI Zhonghui. Algorithm for the HPD confidence interval estimation of parameter of exponential distribution[J]. Journal of Zhejiang University(Science Edition), 2010, 37(5): 515-518.
[14] 茆诗松, 汤银才. 贝叶斯统计[M].北京:中国统计出版社,2012:16-19. MAO Shisong, TANG Yincai. Bayesian statistics[M]. Beijing: China Statistics Press, 2012: 16-19.
[1] LIANG Xiao-lin, GUO Min, LI Jing. Parametric estimations for renewal-geometric process [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 53-57.
[2] YE Jian-hua, MA Ming. Lifetime distribution behavior of discrete open censored δ-shock model [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(04): 8-13.
[3] GAN Xin-jun, YANG Wei-qiang. Weight of evidence method and credit risk control [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(12): 55-59.
[4] ZHANG Quan, HAN Yang, GUAN Bao-ling, LI Yan-jun. Reliability analysis of a warm standby repairable system with unreliable transfer switch [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(10): 62-65.
[5] MA Ming. Computation of the integral of lifetime distribution in the δ-shock model and the properties of the M function [J]. J4, 2008, 43(12): 15-19.
[6] CAO Jing,YUE De-quan . The Gnedenko system attended by a repairman with simple vacations [J]. J4, 2008, 43(6): 77-82 .
[7] SUI Yun-yun, HU Jiang-shan, MA Shu-cai, FU Yun-peng. Parameter estimation of linear exponential distribution based on truncated and censored data [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(6): 10-16.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd