Brazilian Journal of Probability and Statistics

The beta power distribution

Gauss Moutinho Cordeiro and Rejane dos Santos Brito

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Abstract

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.

Article information

Source
Braz. J. Probab. Stat., Volume 26, Number 1 (2012), 88-112.

Dates
First available in Project Euclid: 11 November 2011

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1321043154

Digital Object Identifier
doi:10.1214/10-BJPS124

Mathematical Reviews number (MathSciNet)
MR2871283

Zentralblatt MATH identifier
1230.60011

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

Citation

Moutinho Cordeiro, Gauss; dos Santos Brito, Rejane. The beta power distribution. Braz. J. Probab. Stat. 26 (2012), no. 1, 88--112. doi:10.1214/10-BJPS124. https://projecteuclid.org/euclid.bjps/1321043154


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