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Transmuted Kumaraswamy Distribution

Author

Listed:
  • Robert King
  • Irene Lena Hudson
  • Muhammad Shuaib Khan

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

  • Robert King & Irene Lena Hudson & Muhammad Shuaib Khan, 2016. "Transmuted Kumaraswamy Distribution," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 17(2), pages 183-210, June.
    • Handle: RePEc:csb:stintr:v:17:y:2016:i:2:p:183-210
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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.
    2. William T. Shaw & Ian R. C. Buckley, 2009. "The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map," Papers 0901.0434, arXiv.org.
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    Cited by:

    1. Anum Shafiq & Tabassum Naz Sindhu & Sanku Dey & Showkat Ahmad Lone & Tahani A. Abushal, 2023. "Statistical Features and Estimation Methods for Half-Logistic Unit-Gompertz Type-I Model," Mathematics, MDPI, vol. 11(4), pages 1-24, February.
    2. Devendra Kumar & Manoj Kumar, 2019. "A New Generalization of the Extended Exponential Distribution with an Application," Annals of Data Science, Springer, vol. 6(3), pages 441-462, September.
    3. 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.
    4. M El-Morshedy & Adel A El-Faheem & M El-Dawoody, 2020. "Kumaraswamy inverse Gompertz distribution: Properties and engineering applications to complete, type-II right censored and upper record data," PLOS ONE, Public Library of Science, vol. 15(12), pages 1-23, December.
    5. Sher B. Chhetri & Alfred A. Akinsete & Gokarna Aryal & Hongwei Long, 2017. "The Kumaraswamy transmuted Pareto distribution," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-24, December.
    6. 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.
    7. Weizhong Tian & Liyuan Pang & Chengliang Tian & Wei Ning, 2023. "Change Point Analysis for Kumaraswamy Distribution," Mathematics, MDPI, vol. 11(3), pages 1-22, January.

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