Regression models based on the log-symmetric family of distributions are particularly useful when the response variable is continuous, positive, and asymmetrically distributed. In this article, we propose and derive a class of models based on a new approach to quantile regression using log-symmetric distributions parameterized by means of their quantiles. Two Monte Carlo simulation studies are conducted utilizing the R software. The first one analyzes the performance of the maximum likelihood estimators, the Akaike, Bayesian, and corrected Akaike information criteria, and the generalized Cox–Snell and random quantile residuals. The second one evaluates the size and power of the Wald, likelihood ratio, score, and gradient tests. A web-scraped box-office data set of the movie industry is analyzed to illustrate the proposed approach. Within the main results of the simulation carried out, the good performance of the maximum likelihood estimators is reported.

中文翻译：

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对数对称分位数回归模型

当响应变量是连续的、正的和非对称分布时，基于对数对称分布族的回归模型特别有用。在本文中，我们提出并派生了一类模型，该模型基于一种新的分位数回归方法，该方法使用通过分位数参数化的对数对称分布。利用R进行了两项蒙特卡罗模拟研究软件。第一个分析了最大似然估计量、Akaike、贝叶斯和校正的 Akaike 信息标准以及广义 Cox-Snell 和随机分位数残差的性能。第二个评估 Wald 的大小和功效、似然比、分数和梯度测试。分析了一个网络刮取的电影行业票房数据集，以说明所提出的方法。在所执行的模拟的主要结果中，报告了最大似然估计器的良好性能。