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February 2012 The beta power distribution
Gauss Moutinho Cordeiro, Rejane dos Santos Brito
Braz. J. Probab. Stat. 26(1): 88-112 (February 2012). DOI: 10.1214/10-BJPS124


The power distribution is defined as the inverse of the Pareto distribution. We study in full detail a distribution so-called the beta power distribution. We obtain analytical forms for its probability density and hazard rate functions. Explicit expressions are derived for the moments, probability weighted moments, moment generating function, mean deviations, Bonferroni and Lorenz curves, moments of order statistics, entropy and reliability. We estimate the parameters by maximum likelihood. The practicability of the model is illustrated in two applications to real data.


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Gauss Moutinho Cordeiro. Rejane dos Santos Brito. "The beta power distribution." Braz. J. Probab. Stat. 26 (1) 88 - 112, February 2012.


Published: February 2012
First available in Project Euclid: 11 November 2011

zbMATH: 1230.60011
MathSciNet: MR2871283
Digital Object Identifier: 10.1214/10-BJPS124

Keywords: Beta power distribution , Bonferroni curve , maximum likelihood estimation , moments , order statistic , reliability

Rights: Copyright © 2012 Brazilian Statistical Association

Vol.26 • No. 1 • February 2012
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