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.
出处
《北京工业大学学报》
CAS
CSCD
北大核心
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).
关键词
球极投影变换
Box-Muller公式
正态分布
均匀分布
stereographic projection transformation
Box-Muller formula
normal distribution
uniform distribution
