Brazilian Journal of Probability and Statistics

The exponentiated Kumaraswamy distribution and its log-transform

Artur J. Lemonte, Wagner Barreto-Souza, and Gauss M. Cordeiro

Full-text: Open access

Abstract

The paper by Kumaraswamy (Journal of Hydrology 46 (1980) 79–88) introduced a probability distribution for double bounded random processes which has considerable attention in hydrology and related areas. Based on this distribution, we propose a generalization of the Kumaraswamy distribution refereed to as the exponentiated Kumaraswamy distribution. We derive the moments, moment generating function, mean deviations, Bonferroni and Lorentz curves, density of the order statistics and their moments. We also present a related distribution, so-called the log-exponentiated Kumaraswamy distribution, which extends the generalized exponential (Aust. N. Z. J. Stat. 41 (1999) 173–188) and double generalized exponential (J. Stat. Comput. Simul. 80 (2010) 159–172) distributions. We discuss maximum likelihood estimation of the model parameters. In applications to real data sets, we show that the log-exponentiated Kumaraswamy model can be used quite effectively in analyzing lifetime data.

Article information

Source
Braz. J. Probab. Stat., Volume 27, Number 1 (2013), 31-53.

Dates
First available in Project Euclid: 16 October 2012

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1350394628

Digital Object Identifier
doi:10.1214/11-BJPS149

Mathematical Reviews number (MathSciNet)
MR2991777

Zentralblatt MATH identifier
1319.62032

Keywords
Beta distribution Kumaraswamy distribution maximum likelihood estimation mean deviation order statistic

Citation

Lemonte, Artur J.; Barreto-Souza, Wagner; Cordeiro, Gauss M. The exponentiated Kumaraswamy distribution and its log-transform. Braz. J. Probab. Stat. 27 (2013), no. 1, 31--53. doi:10.1214/11-BJPS149. https://projecteuclid.org/euclid.bjps/1350394628


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