Log symmetric distributions are useful in modeling data which show high skewness and have found applications in various fields. Using a recent characterization for log symmetric distributions, we propose a goodness of fit test for testing log symmetry. The asymptotic distributions of the test statistics under both null and alternate distributions are obtained. As the normal-based test is difficult to implement, we also propose a jackknife empirical likelihood (JEL) ratio test for testing log symmetry. We conduct a Monte Carlo Simulation to evaluate the performance of the JEL ratio test. Finally, we illustrated our methodology using different data sets.

翻译：对数对称分布在建模具有高度偏态的数据时非常有用，并已在多个领域得到应用。利用对数对称分布的最新特征刻画，我们提出了一种用于检验对数对称性的拟合优度检验方法。我们获得了原假设与备择假设下检验统计量的渐近分布。由于基于正态性的检验难以实施，我们还提出了一种用于检验对数对称性的刀切经验似然比检验方法。我们通过蒙特卡洛模拟评估了JEL比检验的性能。最后，我们使用不同数据集对所提方法进行了实例验证。