New insights into non-central beta distributions

TL;DR

This paper provides new mathematical insights into non-central beta distributions, including novel representations and moments, and demonstrates their usefulness in modeling data near the interval endpoints.

Contribution

The paper introduces new representations and moments for non-central beta distributions and explores their advantages over traditional beta models.

Findings

Derived new representations of non-central beta distributions

Provided explicit moments expressions for the distributions

Applied models to real data showing improved fit near endpoints

Abstract

The beta family owes its privileged status within unit interval distributions to several relevant features such as, for example, easyness of interpretation and versatility in modeling different types of data. However, its flexibility at the unit interval endpoints is poor enough to prevent from properly modeling the portions of data having values next to zero and one. Such a drawback can be overcome by resorting to the class of the non-central beta distributions. Indeed, the latter allows the density to take on arbitrary positive and finite limits which have a really simple form. That said, new insights into such class are provided in this paper. In particular, new representations and moments expressions are derived. Moreover, its potential with respect to alternative models is highlighted through applications to real data.