Models for generalized spherical and related distributions

TL;DR

This paper introduces a flexible multivariate generalized spherical distribution model with star-shaped level sets, along with algorithms for simulation and implementation in an R package, enabling advanced geometric and statistical analysis.

Contribution

It develops a new model for multivariate generalized spherical distributions with star-shaped level sets and provides algorithms for simulation, implemented in an R package.

Findings

Successful implementation of the model in R package gensphere

Development of a novel tessellation simulation algorithm

Applicability of techniques to other geometric problems

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.