负二项分布参数的贝叶斯区间估计问题  

Research of the Bayesian Interval Estimate on the Parameter of Negative Binomial Distribution

作　　者：姜培华[1] 纪习习[1] 吴玲[1] 

机构地区：[1]安徽工程大学数理学院,安徽芜湖241000

出　　处：《南通大学学报（自然科学版）》2014年第2期85-90,共6页Journal of Nantong University(Natural Science Edition)　

基　　金：国家自然科学基金项目(11226218);2012年地方高校国家级大学生创新创业训练计划项目(201210363122);安徽省自然科学基金项目(1208085QA04)

摘　　要：研究了在先验分布为贝塔分布下,负二项分布未知参数θ的贝叶斯区间估计方法.借助Beta分布与F分布的关系给出了参数θ的一般后验区间估计,并给出了参数θ的最短后验区间估计的条件极值解法.通过对参数取值不同的密度曲线形状的讨论分析和数值实例对比,得出结论:在小样本情况下,最短置信区间估计方法值得采用.In terms of prior distribution of Beta distribution, the Bayesian estimation method on the unknown parame-ter θ of negative binomial distribution was studied. By means of the relations between Beta distribution and the F dis-tribution the general posterior interval estimation of parameter θ was given, and the shortest posterior interval estima-tion by means of conditional extreme was gained. By comparing the discussion analysis and numerical examples den-sity curve shape of the different parameters, it was concluded that in the case of small samples, the shortest confi-dence interval estimation method is worth using.

关 键 词：负二项分布 贝叶斯估计 贝塔分布 区间估计 

分 类 号：O212.1[理学—概率论与数理统计]