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Statistics in Transition New Series

Polish Statistical Association

Central Statistical Office of Poland

Subject: Economics , Statistics & Probability


ISSN: 1234-7655
eISSN: 2450-0291





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VOLUME 17 , ISSUE 2 (June 2016) > List of articles


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:

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 (𝑇𝐾𝑀) 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 𝑇𝐾𝑀 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.

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