左截断右删失数据中泊松分布的贝叶斯推断

doi:10.6040/j.issn.1671-9352.0.2020.390

《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (7): 46-52.doi: 10.6040/j.issn.1671-9352.0.2020.390

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左截断右删失数据中泊松分布的贝叶斯推断

胡江山¹,隋云云¹,付云鹏²

1. 潍坊学院数学与信息科学学院, 山东潍坊 261061;2. 辽宁大学经济学院, 辽宁沈阳 110036

发布日期:2021-07-19
作者简介:胡江山(1979— ),男,硕士,讲师,研究方向为应用统计研究. E-mail:hjs0501@126.com
基金资助:
国家自然科学基金资助项目(11401438);山东省社科规划项目(17CCXJ14)

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

HU Jiang-shan¹, SUI Yun-yun¹, FU Yun-peng²

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

摘要/Abstract

摘要： 研究了左截断右删失数据中泊松分布的贝叶斯推断问题。主要给出了参数的极大似然估计和贝叶斯估计,同时给出了相应的置信区间。最后给出了贝叶斯推断的随机模拟检验,通过检验发现:在小样本的情况下,贝叶斯估计精度比极大似然估计的精度高一些,而在大样本的情况下,这2种估计的精度相差不大。在置信区间的构造方面,不论是小样本还是大样本,最大后验密度置信区间确实比传统的置信区间有效。

关键词: 贝叶斯估计, 先验分布, 置信区间

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

中图分类号:

O213

胡江山,隋云云,付云鹏. 左截断右删失数据中泊松分布的贝叶斯推断[J]. 《山东大学学报(理学版)》, 2021, 56(7): 46-52.

HU Jiang-shan, SUI Yun-yun, FU Yun-peng. Bayesian inference of Poisson distribution based on left truncated and right censored data[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(7): 46-52.

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左截断右删失数据中泊松分布的贝叶斯推断

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

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