Continuous and strictly positive data that exhibit skewness and outliers frequently arise in many applied disciplines. Log-symmetric distributions provide a flexible framework for modeling such data. In this article, we develop new goodness-of-fit tests for log-symmetric distributions based on a recent characterization. These tests utilize the characteristic function as a novel tool and are constructed using an $L^2$-type weighted distance measure. The asymptotic properties of the resulting test statistic are studied. The finite-sample performance of the proposed method is assessed via Monte Carlo simulations and compared with existing procedures. The results under a range of alternative distributions indicate superior empirical power, while the proposed test also exhibits substantial computational efficiency compared to existing methods. The methodology is further illustrated using real data sets to demonstrate practical applicability.

翻译：在许多应用学科中，经常出现连续、严格为正且呈现偏态和异常值的数据。对数对称分布为建模此类数据提供了一个灵活的框架。本文基于一种近期提出的刻画，开发了对数对称分布的新拟合优度检验。这些检验利用特征函数作为一种新工具，并通过 $L^2$ 型加权距离度量构建。研究了所得检验统计量的渐近性质。通过蒙特卡洛模拟评估了所提方法的有限样本性能，并与现有方法进行了比较。在一系列备择分布下的结果表明，该方法具有更优的经验功效，同时与现有方法相比，所提检验还表现出显著的计算效率。通过实际数据集进一步说明了该方法，以展示其实际适用性。