On a goodness of fit test for the Cauchy distribution

TL;DR

This paper introduces a new goodness-of-fit test for the Cauchy distribution based on characteristic functions, demonstrating its high power through theoretical properties and simulation results.

Contribution

It proposes a novel test statistic derived from a characterization of the Cauchy distribution, enhancing goodness-of-fit testing methods.

Findings

Test is highly powerful against various alternatives

Properties of the test are thoroughly discussed

Simulation studies confirm effectiveness

Abstract

The paper discusses a test for the hypothesis that a random sample comes from the Cauchy distribution. The test statistics is derived from a characterization and is based on the characteristic function. Properties of the test are discussed and its performance measured by simulations. The test presented turns out to be extremely powerful in a wide range of alternatives.