Beta广义Marshall-Olkin-G分布族
The Beta Generalized Marshall-Olkin-G Family of Distributions
摘要：
本文在Beta-G构造族中，以广义Marshal-Olkin分布为基线分布，提出了一个新的分布族。新家族包括Beta-G（Eugene等人，2002年和Jones，2004年）和（Jayakumar和Mathew，2008年）家族作为特殊情况。密度函数（pdf）和累积分布函数（cdf）表示为Marshal-Olkin（Marshal和Olkin，1997）分布的混合。并得到了顺序统计量的pdf的级数展开式。研究了矩、矩母函数、Rényi熵、分位数幂级数、随机样本生成和渐近线。文中还介绍了用极大似然法和矩量法进行参数估计的方法。最后，通过考虑三个实际数据集的数据拟合示例，将所提出的模型与广义Marshall-Olkin Kumaraswamy扩展族（Handique和Chakraborty，2015）进行了比较。
英文摘要：
In this paper we propose a new family of distribution considering Generalized Marshal-Olkin distribution as the base line distribution in the Beta-G family of Construction. The new family includes Beta-G (Eugene et al. 2002 and Jones, 2004) and (Jayakumar and Mathew, 2008) families as particular cases. Probability density function (pdf) and the cumulative distribution function (cdf) are expressed as mixture of the Marshal-Olkin (Marshal and Olkin, 1997) distribution. Series expansions of pdf of the order statistics are also obtained. Moments, moment generating function, Rényi entropies, quantile power series, random sample generation and asymptotes are also investigated. Parameter estimation by method of maximum likelihood and method of moment are also presented. Finally proposed model is compared to the Generalized Marshall-Olkin Kumaraswamy extended family (Handique and Chakraborty, 2015) by considering three data fitting examples with real life data sets.
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