Jackknife empirical likelihood ratio test for log symmetric distribution using probability weighted moments

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.