Modeling with a Large Class of Unimodal Multivariate Distributions

TL;DR

This paper introduces a new flexible class of multivariate unimodal distributions based on Khintchine's representation, with inference algorithms and practical illustrations for real data applications.

Contribution

It proposes a novel unimodal distribution class applicable to multivariate data, extending univariate models with Gaussian copulas and providing inference methods.

Findings

The model covers all univariate unimodal distributions.

MCMC algorithms enable effective inference.

Illustrations demonstrate practical applicability.

Abstract

In this paper we introduce a new class of multivariate unimodal distributions, motivated by Khintchine's representation. We start by proposing a univariate model, whose support covers all the unimodal distributions on the real line. The proposed class of unimodal distributions can be naturally extended to higher dimensions, by using the multivariate Gaussian copula. Under both univariate and multivariate settings, we provide MCMC algorithms to perform inference about the model parameters and predictive densities. The methodology is illustrated with univariate and bivariate examples, and with variables taken from a real data-set.