Entropy-Type Goodness-of-Fit Tests for Heavy-Tailed Distributions

Abstract

The maximum entropy principle is a criterion for selecting a priori probabilities. Maximum entropy modeling has been successfully applied to computer vision, spatial physics, natural language processing and many other fields. Goodness-of-fit (gof) tests measure the degree of agreement between the distribution of an observed random sample and a theoretical statistical distribution. This chapter proposes an alternative information measure that generalizes and is designed for gof tests for heavy-tailed distributions. The chapter provides the test statistic and its asymptotic distribution under the null hypothesis. The power of the test together with the size is the key factor in deciding if the increase in the number of classes is useful. The chapter also provides some simulation studies in order to explore the capabilities of the proposed test statistic. It considers various continuous distributions and applies the probability integral transformation. © ISTE Ltd 2014. All rights reserved.