A Novel Goodness-of-Fit Test for Cauchy Distribution

Abstract

Recently, several goodness-of-fit tests for Cauchy distribution have been introduced based on Kullback–Leibler divergence and likelihood ratio. It is claimed that these tests are more powerful than the well-known goodness-of-fit tests such as Kolmogorov–Smirnov, Anderson–Darling, and Cramér–von Mises under some cases. In this study, a novel goodness-of-fit test is proposed for the Cauchy distribution and the asymptotic null distribution of the test statistic is derived. The critical values of the proposed test are also determined through a Monte Carlo simulation for different sample sizes. The power analysis shows that the proposed test is more powerful than the current tests under certain cases.