The Open Mathematics, Statistics and Probability Journal

2018, 9 : 18-25
Published online 2018 July 31. DOI: 10.2174/1876527001809010017
Publisher ID: TOSPJ-9-18

RESEARCH ARTICLE
 Kumaraswamy Distribution and Random Extrema

Tomasz J. Kozubowski1, * and Krzysztof Podgórski2
1 Department of Mathematics & Statistics, , Reno, NV,
2 Department of Statistics, , Lund,

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

ABSTRACT

Objective:

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.

Result:

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.