Application of Stereographic Projection Transformation in Statistics

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 R^d 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.