p-范分布的参数假设检验  

Parametric Hypothesis Test of p-Norm Distribution

作　　者：胡宏昌 陈璐 HU Hongchang;CHEN Lu(School of Mathematics and Statistics,Hubei Normal University,Huangshi 435002,Hubei,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：《武汉大学学报（理学版）》2021年第2期173-178,共6页Journal of Wuhan University:Natural Science Edition

基　　金：国家自然科学基金(11471105)。

摘　　要：p-范分布是包含拉普拉斯分布、正态分布、均匀分布、退化分布等在内的一类重要分布,然而几乎没有针对该分布的检验问题的研究。探讨了p-范分布中未知参数的假设检验,利用矩估计、极大似然估计和中心极限定理等工具研究了一个和两个总体为p-范分布的未知参数的检验问题。参数μ和p采用近似U检验,单总体方差参数σ采用χp检验,而两个总体的方差参数是否相等采用Fp检验,并用6个模拟算例和1个实例说明了本文的检验方法是可行的。给出了需要进一步研究的两个开问题。p-norm distribution is a kind of distribution, including Laplace distribution, normal distribution, uniform distribution, degenerate distribution, and so on. However, there is little research on the test of this distribution. In this paper, we study the hypothesis test of unknown parameters in the p-norm distribution. Using the tools of moment estimation, maximum likelihood estimation and the central limit theorem, we investigate the unknown parameters test of p-norm distribution under single population and double populations. The parameters μ and p are tested by approximate U-test, and the variance parameter σ of single population are tested by χp-test. For variance parameters of two populations, whether to be equal or not are tested by Fp-test. Six simulation examples and one real case show that our test method is feasible. Finally, two open problems that need further study are given.

关 键 词：P-范分布 参数假设检验 近似U检验 χp检验 Fp检验 

分 类 号：O211.3[理学—概率论与数理统计]