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

Abdulhakim A. Al-Babtain, Ibrahim Elbatal, Christophe Chesneau and Farrukh Jamal
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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

Mathematics, 2020, vol. 8, issue 10, 1-24

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.

Keywords: generalized distribution; Box-Cox transformation; mathematical properties; maximum likelihood estimation; half-Cauchy distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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