A unified testing approach for log-symmetry using Fourier methods

Continuous and strictly positive data that exhibit skewness and outliers frequently arise in many applied disciplines. Log-symmetric distributions provide a flexible framework for modelling 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 L2-type weighted distance measure. The asymptotic properties of the resulting test statistic are studied. Finite-sample performance is examined through Monte Carlo simulations and compared with existing methods, where the results under various alternatives indicate superior empirical power. The methodology is further illustrated using real data sets to demonstrate practical applicability.