In this paper, we introduced a new extension of the beta generator of distributions. Some important properties of the model are discussed, such as the series representation, quantile function, moments, Rényi entropy, and order statistics. Three special members are discussed, namely, the new extended beta exponential (NEBE), new extended beta uniform (NEBU), and new extended beta half logistic (NEBH). The model parameters estimation was achieved by the method of maximum likelihood and the Bayes estimation under square error loss function (SEL); the estimators were examined by simulation studies and it was a very good result as discussed by the bias and mean square error (MSE) of the estimators. Two real data applications are provided to illustrate the importance of the new model in practice.

中文翻译：

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分布的 beta 生成器的新扩展

在本文中，我们介绍了分布的 beta 生成器的新扩展。讨论了模型的一些重要属性，例如级数表示、分位数函数、矩、Rényi 熵和阶数统计。讨论了三个特殊成员，即新的扩展 beta 指数 (NEBE)、新的扩展 beta 统一 (NEBU) 和新的扩展 beta 半逻辑 (NEBH)。模型参数估计采用最大似然法和平方误差损失函数（SEL）下的贝叶斯估计实现；通过模拟研究对估计量进行了检查，正如估计量的偏差和均方误差 (MSE) 所讨论的那样，这是一个非常好的结果。提供了两个真实的数据应用来说明新模型在实践中的重要性。