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A Modified Power Family of Distributions: Properties, Simulations and Applications

Author

Listed:
  • Mohamed Hussein

    (Department of Mathematics and Computer Science, Alexandria University, Alexandria 21544, Egypt
    Department of Business Administration, College of Business, King Khalid University, Abha 61421, Saudi Arabia)

  • Gauss M. Cordeiro

    (Departamento de Estatística, Universidade Federal de Pernambuco, Cidade Universitária, Recife 520740, Brazil)

Abstract

In this paper, we present a new class of distributions called the modified power family by adding an extra shape parameter. Some of its structural properties are derived. Three special cases of the new family are considered and estimated using the method of maximum likelihood. The validity of the method of maximum likelihood is illustrated via Monte Carlo simulations. The importance and flexibility of the new family are empirically illustrated, partly due to efficient modeling of several real data. We compare the proposed family with some distributions and special models generated from other classes using classical statistical measures.

Suggested Citation

  • Mohamed Hussein & Gauss M. Cordeiro, 2022. "A Modified Power Family of Distributions: Properties, Simulations and Applications," Mathematics, MDPI, vol. 10(7), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1035-:d:778302
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    References listed on IDEAS

    as
    1. Abbas Mahdavi & Debasis Kundu, 2017. "A new method for generating distributions with an application to exponential distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(13), pages 6543-6557, July.
    2. Nadarajah, Saralees & Kotz, Samuel, 2006. "The beta exponential distribution," Reliability Engineering and System Safety, Elsevier, vol. 91(6), pages 689-697.
    3. M. E. Ghitany & E. K. Al-Hussaini & R. A. Al-Jarallah, 2005. "Marshall-Olkin extended weibull distribution and its application to censored data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(10), pages 1025-1034.
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