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Box-Cox Gamma-G Family of Distributions: Theory and Applications

Author

Listed:
  • Abdulhakim A. Al-Babtain

    (Department of Statistics and Operations Research, King Saud University, Riyadh 11362, Saudi Arabia)

  • Ibrahim Elbatal

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia)

  • Christophe Chesneau

    (Department of Mathematics, Université de Caen, LMNO, Campus II, Science 3, 14032 Caen, France)

  • Farrukh Jamal

    (Department of Statistics, The Islamia University of Bahawalpur, Punjab 63100, Pakistan)

Abstract

This paper is devoted to a new class of distributions called the Box-Cox gamma-G family. It is a natural generalization of the useful Risti?–Balakrishnan-G family of distributions, containing a wide variety of power gamma-G distributions, including the odd gamma-G distributions. The key tool for this generalization is the use of the Box-Cox transformation involving a tuning power parameter. Diverse mathematical properties of interest are derived. Then a specific member with three parameters based on the half-Cauchy distribution is studied and considered as a statistical model. The method of maximum likelihood is used to estimate the related parameters, along with a simulation study illustrating the theoretical convergence of the estimators. Finally, two different real datasets are analyzed to show the fitting power of the new model compared to other appropriate models.

Suggested Citation

  • Abdulhakim A. Al-Babtain & Ibrahim Elbatal & Christophe Chesneau & Farrukh Jamal, 2020. "Box-Cox Gamma-G Family of Distributions: Theory and Applications," Mathematics, MDPI, vol. 8(10), pages 1-24, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1801-:d:429027
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    References listed on IDEAS

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    1. Pedro Rafael D Marinho & Rodrigo B Silva & Marcelo Bourguignon & Gauss M Cordeiro & Saralees Nadarajah, 2019. "AdequacyModel: An R package for probability distributions and general purpose optimization," PLOS ONE, Public Library of Science, vol. 14(8), pages 1-30, August.
    2. Maha A Aldahlan & Farrukh Jamal & Christophe Chesneau & Ibrahim Elbatal & Mohammed Elgarhy, 2020. "Exponentiated power generalized Weibull power series family of distributions: Properties, estimation and applications," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-25, March.
    3. Ayman Alzaatreh & Carl Lee & Felix Famoye, 2013. "A new method for generating families of continuous distributions," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 63-79, June.
    4. Gauss M. Cordeiro & Morad Alizadeh & Edwin M. M. Ortega, 2014. "The Exponentiated Half-Logistic Family of Distributions: Properties and Applications," Journal of Probability and Statistics, Hindawi, vol. 2014, pages 1-21, March.
    5. José María Sarabia, 2008. "Parametric Lorenz Curves: Models and Applications," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 9, pages 167-190, Springer.
    6. Kus, Coskun, 2007. "A new lifetime distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4497-4509, May.
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