基于贝塔分布的最优置信区间研究  

The Study on Optimal Confidence Interval Based on Beta Distribution

作　　者：温利民[1] 张良超 章溢 刘蔚 WEN Limin;ZHANG Liangchao;ZHANG Yi;LIU Wei(School of Mathematics and Statistics,Jiangxi Normal University,Nanchang Jiangxi 330022,China;School of Finance,Jiangxi Normal University,Nanchang Jiangxi 330022,China)

机构地区：[1]江西师范大学数学与统计学院,江西南昌330022 [2]江西师范大学财政金融学院,江西南昌330022

出　　处：《江西师范大学学报（自然科学版）》2022年第4期342-348,共7页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(72263019);江西省学位与研究生教育教学改革课题(JXYJG-2021-066)资助项目。

摘　　要：基于贝塔分布的概率特征性质,该文研究了一类特殊的贝塔分布的最优区间估计;进而,将得到的区间估计与等尾置信区间进行了比较.结果表明:使用最短置信区间作为未知参数的区间估计,估计的精度得到显著提高.最后,利用数值模拟的方法给出了贝塔分布的最短区间估计用表.Based on the probability properties of the beta distribution,the optimal interval estimation of a special kind of Beta distribution is considered.Furthermore,the obtained interval estimates are compared with equal-tailed confidence intervals.The results show that using the shortest confidence interval as the interval estimation of unknown parameters,the accuracy of the estimation is significantly improved.Finally,a table for estimating the shortest interval of the beta distribution is given by means of numerical simulation.

关 键 词：贝塔分布 等尾置信区间 最短置信区间 

分 类 号：O211.9[理学—概率论与数理统计]