P-范分布尺度参数的似然比检验及其应用  

LIKELIHOOD RATIO TESTS FOR SCALE PARAMETER IN P-NORM DISTRIBUTION AND ITS APPLICATIONS

作　　者：胡宏昌 任欢 HU Hong-chang;REN Huan(School of Mathematics and Statistics,Hubei Normal University,Huangshi 435002,China)

机构地区：[1]湖北师范大学数学与统计学院,湖北黄石435002

出　　处：《数学杂志》2022年第6期493-502,共10页Journal of Mathematics

基　　金：国家自然科学基金资助项目(11471105).

摘　　要：P-范分布包含拉普拉斯分布、正态分布、均匀分布、退化分布等在内的一类重要分布,本文用似然比检验方法研究了该分布中未知尺度参数的检验问题.首先,介绍三个与P-范分布有密切关系的抽样分布;然后,用似然比检验方法研究了一个和两个总体为P-范分布的未知尺度参数的检验问题,得到了似然比检验检验统计量的渐近分布及其(近似)密度函数,并给出了拉普拉斯分布、正态分布等特殊情形下的(近似)密度函数;最后,给出了一些模拟算例来验证本文方法的有效性.P-norm distribution is a important distribution family,including Laplace distribution,normal distribution,uniform distribution,one-point distribution,etc.In this article,we consider the problem of testing scale parameter in P-norm distribution via likelihood ratio test method.Firstly,we introduce three sampling distributions,whose are closely related to P-norm distribution.Secondly,for a and two P-norm distributions,we investigate two hypothesis testing problems of unknown scale parameters by the likelihood ratio test method.We discuss the asymptotic distributions and(approximate)density functions of likelihood ratio test statistics,and also give the(approximate)density functions under some special cases such as Laplace distribution and normal distribution.At last,the validity of our method is illuminated by some numerical examples.

关 键 词：P-范分布 似然比检验 尺度参数 

分 类 号：O212.2[理学—概率论与数理统计]