Beta Generalized Models

The beta transformation gives a great variety of shapes which allow to model symmetric, skewed and bimodal shaped densities. Such procedure generates what we call the beta generalized (beta-G) family of distributions. This chapter presents a survey on the beta-G models and their mathematical properties. We present some explicit expressions for the ordinary and incomplete moments, probability weighted moments, cumulants and generating function, mean deviations, entropies and order statistics.

Keywords: Beta-G model; Entropy; Mean deviation; Moment; Probability weighted moment; Regression model.