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

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 the ideas of Neal (Ann stat 31(3):705–767, 2003) and Ho et al. (J Stat Plan Inference 142(1):25–40, 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., in J Multivar Anal 189(104):944, 2022). Examples and an application to environmental spatial data illustrate its usefulness. Methods are available for free in the new R library relliptical.