A Novel Goodness-of-Fit Test for Cauchy Distribution

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 Cramer-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.

Automated summary

Recently, new goodness-of-fit tests based on Kullback-Leibler divergence and likelihood ratio have been introduced for the Cauchy distribution, claiming to be more powerful than traditional tests. This study proposes a novel test for the Cauchy distribution and derives its asymptotic null distribution. Critical values are determined through Monte Carlo simulation for various sample sizes, and power analysis reveals the superiority of the proposed test under certain conditions.