井冈山大学学报（自然科学版）2026，Vol.47Issue(5)：1-11,11.DOI:10.3969/j.issn.1674-8085.2026.05.001
共轭先验下广义指数分布形状参数的Bayes分析
Bayes analysis for the shape parameter of generalized exponential distribution under conjugate prior
摘要
Abstract
The Bayesian estimations problem of the shape parameter in generalized exponential distribution under the weighted p and q symmetric entropy loss functions were explored.The general and precise forms of Bayesian estimation of the shape parameter with the conjugate gamma prior distribution was obtained,and the uniqueness and admissibility of the estimation were proved.On this basis,the exact forms of the multi-layer Bayesian estimation,empirical Bayesian estimation,and jackknife Bayesian estimation of the shape parameter were further derived.Finally,numerical simulations were conducted using R software and MCMC algorithm.The results show that the jackknife Bayesian estimation under the conjugate prior is superior to the traditional Bayesian estimation and has better robustness;compared with several other loss functions,the Bayesian estimation derived under this specific loss function exhibits higher accuracy.关键词
广义指数分布/加权p,q对称熵损失函数/共轭先验分布/Bayes估计/MCMC算法Key words
generalized exponential distribution/weighted p,q symmetric entropy loss function/conjugate prior distribution/Bayesian estimation/MCMC algorithm分类
数理科学引用本文复制引用
孙霈榆,徐宝..共轭先验下广义指数分布形状参数的Bayes分析[J].井冈山大学学报（自然科学版）,2026,47(5):1-11,11.基金项目
国家自然科学基金项目(11571138) （11571138）
吉林省科技发展计划项目(YDZJ202201ZYTS622) （YDZJ202201ZYTS622）
