The beta family owes its privileged status within unit interval distributions to several relevant features such as, for example, easiness of interpretation and versatility in modeling different types of data. However, the flexibility of its density at the endpoints of the support is poor enough to prevent from properly modeling the data portions having values next to zero and one. Such a drawback can be overcome by resorting to the class of the noncentral beta distributions. Indeed, the latter allows the density to take on arbitrary positive and finite limits which have a really simple form. Nevertheless, the analytical and mathematical complexity of this distribution poses strong limitations on its use as a model for data on the real interval (0, 1). That said, an in-depth study of a newly found analogue of the noncentral beta distribution is carried out in this article. The latter preserves the applicative potential of the standard noncentral beta class but with the advantage of showing a more straightforward and easily handleable density.

中文翻译：

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关于条件非中心贝塔分布

Beta 系列在单位区间分布中的优势地位归功于几个相关特征，例如，易于解释和对不同类型数据建模的多功能性。然而，其在支撑端点处的密度的灵活性很差，以至于无法正确地对具有接近零和一的值的数据部分进行建模。这种缺点可以通过求助于非中心 beta 分布来克服。事实上，后者允许密度具有任意正的和有限的极限，它们具有非常简单的形式。然而，这种分布的分析和数学复杂性对其作为真实区间 (0, 1) 数据模型的使用提出了很大的限制。也就是说，本文对新发现的非中心 beta 分布类似物进行了深入研究。后者保留了标准非中心 beta 类的应用潜力，但具有显示更直接和易于处理的密度的优点。