Open Access
February 2013 The exponentiated Kumaraswamy distribution and its log-transform
Artur J. Lemonte, Wagner Barreto-Souza, Gauss M. Cordeiro
Braz. J. Probab. Stat. 27(1): 31-53 (February 2013). DOI: 10.1214/11-BJPS149


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.


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Artur J. Lemonte. Wagner Barreto-Souza. Gauss M. Cordeiro. "The exponentiated Kumaraswamy distribution and its log-transform." Braz. J. Probab. Stat. 27 (1) 31 - 53, February 2013.


Published: February 2013
First available in Project Euclid: 16 October 2012

zbMATH: 1319.62032
MathSciNet: MR2991777
Digital Object Identifier: 10.1214/11-BJPS149

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

Rights: Copyright © 2013 Brazilian Statistical Association

Vol.27 • No. 1 • February 2013
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