A unified testing approach for log-symmetry using Fourier methods

TL;DR

This paper introduces new goodness-of-fit tests for log-symmetric distributions using Fourier methods, demonstrating superior power and efficiency through simulations and real data applications.

Contribution

It develops a novel Fourier-based testing procedure for log-symmetric distributions, leveraging a recent characterization and characteristic function approach.

Findings

Tests show higher empirical power than existing methods

Proposed tests are computationally efficient

Effective in real data applications

Abstract

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.