New Properties of the Kumaraswamy Distribution

The Kumaraswamy distribution is very similar to the Beta distribution but has the key advantage of a closed-form cumulative distribution function. This makes it much better suited than the Beta distribution for computation-intensive activities like simulation modeling and the estimation of models by simulation-based methods. However, in spite of the fact that the Kumaraswamy distribution was introduced in 1980, further theoretical research on the distribution was not developed until very recently (Garg, 2008 Garg , M. ( 2008 ). On distribution of order statistics from Kumaraswamy distribution . Kyunpook Mathemat. J. 48 : 411 – 417 .[Crossref] , [Google Scholar]; Jones, 2009 Jones , M. C. ( 2009 ). Kumaraswamy's distribution: A beta-type distribution with some tractability advantages . Statist. Methodol. 6 ( 1 ): 70 – 81 .[Crossref] , [Google Scholar]; Mitnik, 2009 Mitnik , P. ( 2009 ). The Kumaraswamy distribution: a median-dispersion re-parameterization for regression modeling and simulation-based estimation. Available at SSRN: http://ssrn.com/abstract=1231587 . [Google Scholar]; Nadarajah, 2008 Nadarajah , S. ( 2008 ). On the distribution of Kumaraswamy . J. Hydrol. 348 : 568 – 569 .[Crossref], [Web of Science ®] , [Google Scholar]). This article contributes to this recent research and: (a) shows that Kumaraswamy variables exhibit closeness under exponentiation and under linear transformation; (b) derives an expression for the moments of the general form of the distribution; (c) specifies some of the distribution's limiting distributions; and (d) introduces an analytical expression for the mean absolute deviation around the median as a function of the parameters of the distribution, and establishes some bounds for this dispersion measure and for the variance.