| 球极投影变换在统计中的应用 |
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| 引用本文： | 赵颖.球极投影变换在统计中的应用[J].北京工业大学学报,2004,30(1):120-123. |
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| 作者姓名： | 赵颖 |
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| 作者单位： | 北京工业大学,应用数理学院,北京,100022 |
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| 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.
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| 关 键 词： | 球极投影变换 Box-Muller公式 正态分布 均匀分布 |
| 文章编号： | 0254-0037(2004)01-0120-04 |
| 修稿时间： | 2003年4月15日 |
Application of Stereographic Projection Transformation in Statistics |
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| ZHAO Ying.Application of Stereographic Projection Transformation in Statistics[J].Journal of Beijing Polytechnic University,2004,30(1):120-123. |
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| Authors: | ZHAO Ying |
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| Abstract: | 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. |
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| Keywords: | stereographic projection transformation Box-Muller formula normal distribution uniform distribution |
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