A Model for Bimodal Rates and Proportions

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....

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Bibliographic Details
Published inarXiv.org
Main Authors Vila, Roberto, Lucas Alfaia, Menezes, André F B, Çankaya, Mehmet N, Bourguignon, Marcelo
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 18.08.2021
Subjects
Maximum likelihood estimation
Probability distribution functions
Regression models
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Summary: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.
ISSN:2331-8422