Abstract
A geometrical method of constructing multivariate densities, which is based on surface integral techniques, is given. A characterization of spherical and elliptical densities is proved using Che general method, and a particular class of spherical distributions is used to test for spherical normality against spherical alternatives. The method of moments procedure for estimating the parameters of an elliptical density is given. Densities which are constant on subsets of hyperplanes are constructed and an application is suggested. Other examples and applications are also discussed.
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