A new goodness-of-fit test for the Cauchy distribution

What the paper says

This article presents a novel and powerful goodness-of-fit test specifically designed for the Cauchy distribution.The motivation behind our research stems from the need for a more accurate and robust method to assess the fit of the Cauchy distribution to data.This distribution is known for its heavy tails and lack of finite moments.To compute the proposed test statistic, we utilize the maximum likelihood estimators of the unknown parameters, ensuring the test efficiency and reliability.In addition, Monte Carlo simulations are employed to obtain critical points of the test statistic for different sample sizes, enabling precise determination of the threshold for rejecting the null hypothesis.To assess the performance of the proposed test, we conduct power comparisons against several well-known competing tests, considering various alternative distributions.Through extensive simulations, we demonstrate the superiority of our test in the majority of the cases examined, highlighting its effectiveness in distinguishing departures from the Cauchy distribution.The contributions of our study are twofold.Firstly, we introduce a novel goodness-of-fit test tailored specifically for the Cauchy distribution, taking into account its unique characteristics.By incorporating the maximum likelihood estimate and employing Monte Carlo simulations, our test offers improved accuracy and robustness compared to existing methods.Furthermore, we provide practical validation of the proposed test through the analysis of a financial dataset.The application of the test to real-world data underscores its relevance and applicability in practical scenarios.