A Model for Bimodal Rates and Proportions

TL;DR

This paper introduces a new bimodal beta distribution based on the alpha-skew-normal model, addressing the limitations of the traditional beta distribution for bimodal data, and develops a regression model with estimation and validation.

Contribution

It proposes a novel bimodal beta distribution, explores its properties, and develops a regression framework with maximum likelihood estimation and Monte Carlo validation.

Findings

The proposed distribution effectively models bimodal data.

Maximum likelihood estimators perform well in finite samples.

Application demonstrates the model's suitability for bimodal datasets.

Abstract

The beta model is the most important distribution for fitting data with the unit interval. However, the beta distribution is not suitable to model bimodal unit interval data. In this paper, we propose a bimodal beta distribution constructed by using an approach based on the alpha-skew-normal model. We discuss several properties of this distribution such as bimodality, real moments, entropy measures and identifiability. Furthermore, we propose a new regression model based on the proposed model and discuss residuals. Estimation is performed by maximum likelihood. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the results. An application is provided to show the modelling competence of the proposed distribution when the data sets show bimodality.