Box-Cox elliptical distributions with application

TL;DR

This paper introduces the Box-Cox elliptical distributions, a flexible class for modeling multivariate positive, skewed, and heavy-tailed data, with applications demonstrated on vitamin intake data.

Contribution

It develops a new class of distributions that generalizes log-elliptical and Box-Cox symmetric distributions, with interpretable parameters suitable for regression modeling.

Findings

Effective modeling of skewed, heavy-tailed multivariate data.

Parameters linked to quantiles and associations.

Successful application to vitamin intake data.

Abstract

We propose and study the class of Box-Cox elliptical distributions. It provides alternative distributions for modeling multivariate positive, marginally skewed and possibly heavy-tailed data. This new class of distributions has as a special case the class of log-elliptical distributions, and reduces to the Box-Cox symmetric class of distributions in the univariate setting. The parameters are interpretable in terms of quantiles and relative dispersions of the marginal distributions and of associations between pairs of variables. The relation between the scale parameters and quantiles makes the Box-Cox elliptical distributions attractive for regression modeling purposes. Applications to data on vitamin intake are presented and discussed.