Logistic or not Logistic?

Abstract

We propose a new class of goodness-of-fit tests for the logistic distribution based on a characterization related to the density approach in the context of Stein's method. This characterization-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.