In this paper, we introduce a modified family of distributions that unifies three different families with only one tuning parameter; the so-called exp-[Formula: see text], Topp–Leone-[Formula: see text] and exp-half-[Formula: see text] families of distributions. We study mathematical properties of the proposed family, including linear representations, quantile function, probability weighted moments, reliability parameter and stochastic ordering. One of the corresponding parametric statistical model is outlined, with estimation of the parameters by the method of maximum likelihood and investigation for possible applications to glycosaminoglycans concentration level in urine over the beta Weibull and Kumaraswamy Weibull distributions. The goodness-of-fit of five other members of the family is also assessed. Regression model is also discussed using the proposed distribution and applied to establish the relationship between the glycosaminoglycans concentration level and age of the children.

中文翻译：

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扩展的 Topp-Leone 家族分布作为 β 和 Kumaraswamy 型分布的替代品：在尿液中糖胺聚糖浓度水平的应用

在本文中，我们介绍了一个修改后的分布族，它统一了三个不同的族，只有一个调整参数；所谓的 exp-[Formula: see text]、Topp-Leone-[Formula: see text] 和 exp-half-[Formula: see text] 分布族。我们研究了所提出族的数学特性，包括线性表示、分位数函数、概率加权矩、可靠性参数和随机排序。概述了相应的参数统计模型之一，通过最大似然法估计参数，并研究了在 beta Weibull 和 Kumaraswamy Weibull 分布上尿中糖胺聚糖浓度水平的可能应用。还评估了该家庭其他五名成员的拟合优度。