A New Class of Non-Central Dirichlet Distributions

TL;DR

This paper introduces the Conditional Non-central Dirichlet distribution, a more tractable extension of the Dirichlet distribution that better models data near the vertices of the simplex by allowing flexible tail behavior.

Contribution

It proposes a new class of non-central Dirichlet distributions that are easier to work with and can capture data tail behavior more effectively than existing models.

Findings

The new distribution maintains the ability to model tail behavior.

It offers improved tractability over existing non-central Dirichlet models.

The distribution allows arbitrary positive finite limits for the density.

Abstract

In the present paper new light is shed on the non-central extensions of the Dirichlet distribution. Due to several probabilistic and inferential properties and to the easiness of parameter interpretation, the Dirichlet distribution proves the most well-known and widespread model on the unitary simplex. However, despite its many good features, such distribution is inadequate for modeling the data portions next to the vertices of the support due to the strictness of the limiting values of its joint density. To replace this gap, a new class of distributions, called Conditional Non-central Dirichlet, is presented herein. This new model stands out for being a more easily tractable version of the existing Non-central Dirichlet distribution which maintains the ability of this latter to capture the tails of the data by allowing its own density to have arbitrary positive and finite limits.