We study general mathematical properties of a new class of continuous distributions with three extra shape parameters called the exponentiated Marshal-Olkin family of distributions. Further, we present some special models of the new class and investigate the shapes and derive explicit expressions for the ordinary and incomplete moments, quantile and generating functions and probability weighted moments. We discuss the estimation of the model parameters by maximum likelihood and show empirically the potentiality of the family by means of two applications to real data.

中文翻译：

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Marshall-Olkin指数分布家族

我们研究具有三个额外形状参数（称为指数Marshal-Olkin分布族）的新型连续分布的一般数学性质。此外，我们提出了新类的一些特殊模型，并研究了形状并得出了普通和不完整矩，分位数和生成函数以及概率加权矩的显式表达式。我们讨论了通过最大似然估计模型参数的方法，并通过对实际数据的两次应用，通过经验证明了该族的潜力。