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 Ristić–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.

中文翻译：

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Box-Cox Gamma-G分布家族：理论与应用

本文致力于一种称为Box-Cox gamma-G系列的新型分布。它是有用的Ristić–Balakrishnan-G分布族的自然概括，其中包含各种幂次伽马-G分布，包括奇数伽马-G分布。进行这种概括的关键工具是使用Box-Cox变换，该变换涉及调谐功率参数。得出感兴趣的各种数学性质。然后研究基于半柯西分布的具有三个参数的特定成员，并将其视为统计模型。最大似然法用于估算相关参数，并通过仿真研究说明了估算器的理论收敛性。最后，