Weighted Beta Regression for Modeling Bounded Data

A two-parameter weighted beta distribution is introduced for modeling bounded data, which has many similarities to the beta distribution. We propose a class of regression models where the response is weighted beta distributed and the two shape parameters that index the weighted beta distribution are related to covariates and regression parameters. The proposed regression model is a natural strong competitor of the beta regression model. We study the mathematical and statistical properties of the distribution, and we provide a useful interpretation of the parameters. The maximum likelihood method is used for estimating the model parameters. We conduct simulation studies to investigate the performance of the maximum likelihood estimators and the asymptotic confidence intervals of the parameters. We present an application of the proposed regression model to real bounded data.