Goodness-of-fit tests based on a characterization of logistic distribution

Abstract

The logistic family of distributions belongs to the class of important families in Probability and Statistics. However, the goodness-of-fit tests for the composite hypothesis of belonging to the logistic family with unknown location parameter against the general alternatives are almost unexplored. We propose two new goodness-of-fit tests: the integral and Kolmogorov-type, based on the recent characterization of logistic family by Hu and Lin. We discuss asymptotic properties of new tests and calculate their Bahadur efficiency for natural alternatives.