二维正态总体样本相关系数的极限分布  

Limit Distribution of Sample Correlation Coefficient of Two-dimensional Normal Distribution

作　　者：李琼[1] 武东[2] LI Qiong;WU Dong(Department of Electronic Information,Huishang Vocational College,Hefei 231021,China;School of Science,Anhui Agricultural University,Hefei 230036,China)

机构地区：[1]安徽商职业学院,安徽合肥231201 [2]安徽农业大学理学院

出　　处：《通化师范学院学报》2020年第2期21-24,共4页Journal of Tonghua Normal University

基　　金：安徽省高校自然科学研究重点项目(KJ2017A892);安徽省高校优秀青年人才支持计划项目(gxyq2019254)

摘　　要：文章研究了部分参数已知和所有参数未知情况下二维正态总体的样本相关系数,利用大数定律、中心极限定理和Slutsky定理证明了二维正态总体的样本相关系数具有渐近正态性,并获得其极限分布.In this paper,we study the sample correlation coefficients of two-dimensional normal population under some parameters are known and all parameters are unknown.Asymptotically Normal distributions of the sample correlation coefficients of two-dimensional Normal distribution and limit distributions are derived using law of large number,central limit theorem and Slutsky theorem.

关 键 词：二维正态分布 极限分布 中心极限定理 样本相关系数 

分 类 号：O212[理学—概率论与数理统计]