Cauchy分布的统计分析方法研究  

Study on Statistical Analysis Method of Cauchy Distribution

作　　者：顾蓓青 王蓉华[2] 徐晓岭 

机构地区：[1]上海对外经贸大学统计与信息学院,上海201620 [2]上海师范大学数理学院,上海200234

出　　处：《统计与决策》2017年第20期19-22,共4页Statistics & Decision

基　　金：国家自然科学基金资助项目(11671264)

摘　　要：文章在刻度参数λ已知的情形下,给出了位置参数μ的分位数估计与逆矩估计,通过模拟比较发现分位数估计更加精确。同时还给出了参数μ的区间估计,考察了区间估计的精度;在位置参数μ已知的情形下,给出了刻度参数λ的极大似然估计,考察了点估计的精度;在参数μλ都未知的情形下,给出了参数μλ的点估计,通过模拟认为位置参数μ的点估计取样本中位数,而刻度参数λ的点估计取极大似然估计(依赖于μ的估计)较为精确。This paper gives the quantile estimate and inverse moment estimate of location parameter μ in the case of known scale parameter λ, and finds that quantile estimate is more accurate through simulation comparison. At the same time, the interval estimate of parameter λ is given and the precision of interval estimate investigated; the maximum likelihood estimate of scale pa- rameter λ also given in the case of known location parameter μ, and the precision of point estimate investigated; the point esti- mates of parameters μ, λ is provided in the case of unknown parameters μ ,λ ; the paper finds that sample median is more accu- rate for point estimate of location parameter μ, while maximum likelihood estimate depending on estimate of μ is more accurate for point estimate of scale parameter 2.

关 键 词：Cauchy分布 位置参数 刻度参数 逆矩估计 极大似然估计 分位数估计 

分 类 号：O212[理学—概率论与数理统计]