球极投影变换在统计中的应用  

Application of Stereographic Projection Transformation in Statistics

作　　者：赵颖[1] 

机构地区：[1]北京工业大学应用数理学院,北京100022

出　　处：《北京工业大学学报》2004年第1期120-123,共4页Journal of Beijing University of Technology

基　　金：北京自然科学基金资助项目(D080401-01).

摘　　要：为了拓展球极投影变换在数理统计中的应用,采用球极投影变换导出Box-Muller二维变换抽样公式.球极投影变换是建立Rd空间上的点与单位球面上的点的一一对应关系.对于d=2,通过变量代换,利用球极投影变换可以导出Box-Muller公式.进一步推广,对于d>2,可以导出在多元统计分析中占重要地位的球对称分布.The purpose of this study is to use stereographic projection transformation to derive Box-Muller bivariate transformation sampling formula. Stereographic projection trans-formation is to establish one-to-one map between the point in the Rd space and the point on the surface of a unit sphere. Through variable substitution, Box-Muller formula can be derived by means of stereographic projection transformation for d=2. By an extension of this logic, for d>2, the spherical symmetric distribution very important in multivariate statistical analysis can also be derived.

关 键 词：球极投影变换 Box-Muller公式 正态分布 均匀分布 

分 类 号：O213[理学—概率论与数理统计] O174[理学—数学]