Models for generalized spherical and related distributions

Abstract

A flexible model is developed for multivariate generalized spherical distributions, i.e. ones with level sets that are star shaped. To work in dimension above 2 requires tools from computational geometry and multivariate numerical integration. In order to simulate from these star shaped contours, an algorithm to simulate from general tessellations has been developed that has applications in other situations. These techniques are implemented in an R package gensphere.