Polish Statistical Association
Central Statistical Office of Poland
Subject: Economics, Statistics & Probability
ISSN: 1234-7655
eISSN: 2450-0291
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Muhammad Shuaib Khan * / Robert King * / Irene Lena Hudson *
Keywords : Kumaraswamy distribution, moments, order statistics, parameter estimation, maximum likelihood estimation
Citation Information : Statistics in Transition New Series. Volume 17, Issue 2, Pages 183-210, DOI: https://doi.org/10.21307/stattrans-2016-013
License : (CC BY 4.0)
Published Online: 06-July-2017
The Kumaraswamy distribution is the most widely applied statistical distribution in hydrological problems and many natural phenomena. We propose a generalization of the Kumaraswamy distribution referred to as the transmuted Kumaraswamy (ππΎπ€) distribution. The new transmuted distribution is developed using the quadratic rank transmutation map studied by Shaw et al. (2009). A comprehensive account of the mathematical properties of the new distribution is provided. Explicit expressions are derived for the moments, moment generating function, entropy, mean deviation, Bonferroni and Lorenz curves, and formulated moments for order statistics. The ππΎπ€ distribution parameters are estimated by using the method of maximum likelihood. Monte Carlo simulation is performed in order to investigate the performance of MLEs. The flood data and HIV/ AIDS data applications illustrate the usefulness of the proposed model.