Generalized Beta-Generated Distributions

Abstract

This article introduces generalized beta-generated (GBG) distributions. Sub-models include all classical beta-generated, Kumaraswamy-generated and exponentiated distributions. They are maximum entropy distributions under three intuitive conditions, which show that the classical beta generator skewness parameters only control tail entropy and an additional shape parameter is needed to add entropy to the centre of the parent distribution. This parameter controls skewness without necessarily differentiating tail weights. The GBG class also have tractable properties: we present various expansions for moments, generating function, quantiles, deviations and reliability. The model parameters are estimated by maximum likelihood and the usefulness of the new class is illustrated by means of some real data sets.

Keywords: Beta, Distribution, Entropy, Estimation, Exponentiated, Gamma, Generalized,Generated, Gumbel, Inverse Guassian, Kumaraswamy, Kurtosis, Laplace, McDonald, Minimax, MLE, MGF, Reliability, Skewness, Weibull

JEL Classification: C16, G1