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Transmuted Kumaraswamy Distribution

Author

Listed:
  • Khan Muhammad Shuaib

    (School of Mathematical and Physical Sciences, The University of Newcastle, Callaghan, NSW 2308, Australia .)

  • King Robert

    (School of Mathematical and Physical Sciences, The University of Newcastle, Callaghan, NSW 2308, Australia .)

  • Hudson Irene Lena

    (School of Mathematical and Physical Sciences, The University of Newcastle, Callaghan, NSW 2308, Australia .)

Abstract

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 (TKw) 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 TKw 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.

Suggested Citation

  • Khan Muhammad Shuaib & King Robert & Hudson Irene Lena, 2016. "Transmuted Kumaraswamy Distribution," Statistics in Transition New Series, Statistics Poland, vol. 17(2), pages 183-210, June.
    • Handle: RePEc:vrs:stintr:v:17:y:2016:i:2:p:183-210:n:12
    DOI: 10.21307/stattrans-2016-013
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    References listed on IDEAS

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    1. Abbas Seifi & K. Ponnambalam & Jiri Vlach, 2000. "Maximization of Manufacturing Yield of Systems with Arbitrary Distributions of Component Values," Annals of Operations Research, Springer, vol. 99(1), pages 373-383, December.
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    Cited by:

    1. Odom Conleth Chinazom & Nduka Ethelbert Chinaka & Ijomah Maxwell Azubuike, 2019. "The Marshall-Olkin Extended Weibull-Exponential Distribution: Properties and Applications," Journal of Asian Scientific Research, Asian Economic and Social Society, vol. 9(10), pages 158-172, October.
    2. Rashad A. R. Bantan & Christophe Chesneau & Farrukh Jamal & Mohammed Elgarhy & Waleed Almutiry & Amani Abdullah Alahmadi, 2021. "Study of a Modified Kumaraswamy Distribution," Mathematics, MDPI, vol. 9(21), pages 1-26, November.

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