Moments and random number generation for the truncated elliptical family of distributions

TL;DR

This paper introduces an efficient slice sampling algorithm for generating random numbers from truncated multivariate elliptical distributions, along with methods to approximate moments, demonstrated through environmental data analysis.

Contribution

It presents a novel sampling algorithm and moment approximation techniques for truncated elliptical distributions, implemented in the new R package elliptical.

Findings

Efficient sampling method for truncated elliptical distributions.

Approximate moments using Monte Carlo integration.

Application demonstrated on environmental spatial data.

Abstract

This paper proposes an algorithm to generate random numbers from any member of the truncated multivariate elliptical family of distributions with a strictly decreasing density generating function. Based on Neal (2003) and Ho et al. (2012), we construct an efficient sampling method by means of a slice sampling algorithm with Gibbs sampler steps. We also provide a faster approach to approximate the first and the second moment for the truncated multivariate elliptical distributions where Monte Carlo integration is used for the truncated partition, and explicit expressions for the non-truncated part (Galarza et al., 2020). Examples and an application to environmental spatial data illustrate its usefulness. Methods are available for free in the new R library elliptical.