Goodness-of-fit test for Cauchy distribution derived from the empirical characteristic function

Abstract

Two parameter-free tests for Cauchy distributions are constructed based on the specific form of the characteristic function. It is shown that asymptotically both test statistics follow an F_{1, 1} - distribution under the null hypothesis and that they are consistent for symmetric alternatives. The performance of both methods in finite samples is investigated by employing simulated as well as real data.