Kumaraswamy Distribution and Random Extrema

Tomasz J. Kozubowski1, *, Krzysztof Podgórski2
1 Department of Mathematics & Statistics, University of Nevada, Reno, NV, USA
2 Department of Statistics, Lund University, Lund, Sweden

© 2018 Kozubowski et al.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Mathematics & Statistics, University of Nevada, Reno, NV, USA; Tel: 7757846643; E-mail:



We provide a new stochastic representation for a Kumaraswamy random variable with arbitrary non-negative parameters. The representation is in terms of maxima and minima of independent distributed standard uniform components and extends a similar representation for integer-valued parameters.


The result is further extended for generalized classes of distributions obtained from a “base” distribution function Fviz.G(x) = H(F(x)), where H is the CDF of Kumaraswamy distribution.

Keywords: Distortion function, Distribution theory, Extremes, Kumaraswamy generalized distribution, Marshall-Olkin scheme, Proportional hazards transform, Quadratic transmutation map, Random extrema, Sibuya distribution.