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.
This supplementary material provides technical details and their proofs for the analysis in the main text.1 Supplementary Material I. SOME CHARACTERISTICS OF BBETA DISTRIBUTION Corollary 1.1 (Mean residual life function). If X ∼ Bbeta(θ δ ) then mean residual life function of X, defined by MRL(x, θ δ ) =
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