Generalized Beta-Generated Distributions

University of Reading ICMA Centre Finance Discussion Paper No. DP2010-09

30 Pages Posted: 29 Jul 2010 Last revised: 11 Feb 2011

See all articles by Carol Alexander

Carol Alexander

University of Sussex Business School

Gauss Cordeiro

Universidade Federal de Pernambuco (UFPE) - Departmento de Estatistica

Edwin Ortega

University of Sao Paulo (USP)

José María Sarabia

University of Cantabria - Department of Economics

Date Written: July 27, 2010

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

Suggested Citation

Alexander, Carol and Cordeiro, Gauss and Ortega, Edwin and Sarabia, José María, Generalized Beta-Generated Distributions (July 27, 2010). University of Reading ICMA Centre Finance Discussion Paper No. DP2010-09. Available at SSRN: https://ssrn.com/abstract=1650630 or http://dx.doi.org/10.2139/ssrn.1650630

Carol Alexander (Contact Author)

University of Sussex Business School ( email )

Falmer, Brighton BN1 9SL
United Kingdom

HOME PAGE: http://www.carolalexander.org

Gauss Cordeiro

Universidade Federal de Pernambuco (UFPE) - Departmento de Estatistica ( email )

Recife/PE 50740-540
Brazil

Edwin Ortega

University of Sao Paulo (USP) ( email )

José María Sarabia

University of Cantabria - Department of Economics ( email )

Av. Los Castros s/n
39005 - Santander (Cantabria), Cantabria 39005
Spain

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