RESEARCH ARTICLE
Kumaraswamy Distribution and Random Extrema
Tomasz J. Kozubowski1, *, Krzysztof Podgórski2
Article Information
Identifiers and Pagination:
Year: 2018Volume: 9
First Page: 18
Last Page: 25
Publisher Id: TOSPJ-9-18
DOI: 10.2174/1876527001809010017
Article History:
Received Date: 7/3/2018Revision Received Date: 26/6/2018
Acceptance Date: 29/6/2018
Electronic publication date: 31/7/2018
Collection year: 2018
© 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: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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.
