Logistic or not logistic?

TL;DR

This paper introduces a novel goodness-of-fit test for the logistic distribution using Stein's method, demonstrating superior power against heavy-tailed and skewed alternatives through theoretical derivation and simulation studies.

Contribution

It presents the first characterisation-based goodness-of-fit test for the logistic distribution, including derivation of its null distribution and power analysis.

Findings

Test is consistent against fixed alternatives.

Test outperforms existing methods for heavy-tailed and skewed distributions.

Finite sample power is validated through Monte Carlo simulations.

Abstract

We propose a new class of goodness-of-fit tests for the logistic distribution based on a characterisation related to the density approach in the context of Stein's method. This characterisation based test is a first of its kind for the logistic distribution. The asymptotic null distribution of the test statistic is derived and it is shown that the test is consistent against fixed alternatives. The finite sample power performance of the newly proposed class of tests is compared to various existing tests by means of a Monte Carlo study. It is found that this new class of tests are especially powerful when the alternative distributions are heavy tailed, like Student's t and Cauchy, or for skew alternatives such as the log-normal, gamma and chi-square distributions.