Abstract Recent studies have highlighted the statistical relevance and applicability of trigonometric distributions for the modeling of various phenomena. This paper contributes to the subject by investigating a new trigonometric family of distributions defined from the alliance of the families known as sine-G and Topp-Leone generated (TL-G), inspiring the name of sine TL-G family. The characteristics of this new family are studied through analytical, graphical and numerical approaches. Stochastic ordering and equivalence results, determination of the mode(s), some expansions of distributional functions, expressions of the quantile function and moments and basics on order statistics are discussed. In addition, we emphasize the fact that the sine TL-G family is able to generate original, simple and pliant trigonometric models for statistical purposes, beyond the capacity of the former sine-G models and other top models of the literature. This fact is revealed with the special three-parameter sine TL-G model based on the inverse Lomax model, through an efficient parametric estimation and the adjustment of two data sets of interest.

中文翻译：

---

Sine Topp-Leone-G 分布族：理论与应用

摘要 最近的研究强调了三角分布对各种现象建模的统计相关性和适用性。本文通过研究由正弦 G 和 Topp-Leone 生成 (TL-G) 家族的联盟定义的新三角分布家族，为该主题做出了贡献，启发了正弦 TL-G 家族的名称。通过分析、图形和数值方法研究了这个新系列的特性。讨论了随机排序和等价结果、模式的确定、分布函数的一些扩展、分位数函数和矩的表达式以及顺序统计的基础知识。此外，我们强调正弦 TL-G 系列能够生成原始的，用于统计目的的简单而灵活的三角模型，超出了以前的正弦 G 模型和其他顶级文献模型的能力。这一事实通过基于逆 Lomax 模型的特殊三参数正弦 TL-G 模型通过有效的参数估计和两个感兴趣的数据集的调整来揭示。