This work proposes a new distribution defined on the unit interval. It is obtained by a novel transformation of a normal random variable involving the hyperbolic secant function and its inverse. The use of such a function in distribution theory has not received much attention in the literature, and may be of interest for theoretical and practical purposes. Basic statistical properties of the newly defined distribution are derived, including moments, skewness, kurtosis and order statistics. For the related model, the parametric estimation is examined through different methods. We assess the performance of the obtained estimates by two complementary simulation studies. Also, the quantile regression model based on the proposed distribution is introduced. Applications to three real datasets show that the proposed models are quite competitive in comparison to well-established models.

中文翻译：

---

关于反正割双曲正态分布。性质，分位数回归建模和应用

这项工作提出了在单位间隔上定义的新分布。它是通过对包含双曲正割函数及其反函数的正态随机变量进行新颖的变换而获得的。在分布理论中使用这种函数在文献中并未引起太多关注，并且可能在理论和实践目的上引起人们的兴趣。得出新定义的分布的基本统计属性，包括弯矩，偏度，峰度和阶次统计量。对于相关模型，可以通过不同方法检查参数估计。我们通过两个互补的仿真研究评估获得的估计的性能。此外，介绍了基于建议分布的分位数回归模型。