## Brazilian Journal of Probability and Statistics

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

### The beta power distribution

Gauss Moutinho Cordeiro and Rejane dos Santos Brito

#### 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