对数艾拉姆咖分布的统计分析  

Statistical Analysis of Log-Эрланга Distribution

作　　者：常帅 关晋瑞 CHANG Shuai;GUAN Jinrui(School of Mathematics and Statistics,Taiyuan Normal University,Jinzhong 030619,China)

机构地区：[1]太原师范学院数学与统计学院,山西晋中030619

出　　处：《中央民族大学学报（自然科学版）》2022年第4期55-60,共6页Journal of Minzu University of China(Natural Sciences Edition)

基　　金：山西省应用基础研究计划项目(201901D211423);太原师范学院教学改革项目(JGLX2129)。

摘　　要：基于艾拉姆咖分布,提出了一类新的对数艾拉姆咖分布。文中讨论了新分布的若干性质,研究了新分布的参数估计,提出了参数点估计的四种方法:矩估计、极大似然估计、对数矩估计与逆矩估计。通过Monte-Carlo模拟比较了估计的精度,结果表明极大似然估计、对数矩估计与逆矩估计优于矩估计。此外还给出了新分布参数的两种区间估计,Monte-Carlo模拟表明此两种区间估计的精度相当。实例分析说明了除矩估计外所提出的估计方法的可行性。Based on Эрланга distribution, a new class of distribution called log-Эрланга distribution is proposed. Some properties of new distribution are discussed. And this paper studies the parameter estimation of new distribution, proposes four methods of parameter point estimation, including moment estimation, maximum likelihood estimation, log-moment estimation and inverse moment estimation. The accuracy of the estimates was compared by Mont-Carlo simulation. The results show that the maximum likelihood estimator, log-moment estimator and inverse moment estimator are better than moment estimator. In addition, two interval estimators of parameters are given and the accuracy of the two interval estimators is nearly equal by Mont-Carlo simulation. Finally, two examples are used to illustrate the feasibility of the proposed method of estimation except moment estimation.

关 键 词：对数艾拉姆咖分布 矩估计 极大似然估计 对数矩估计 逆矩估计 

分 类 号：O212.1[理学—概率论与数理统计]