Goodness-of-fit tests for the Cauchy distribution
The Cauchy family of distributions is defined by the pdf \[ f(x)=[\pi\psi(1+(x-\lambda)\psi^{-1})]^{-2}, \] where \(\lambda\) and \(\psi\) are the location and scale parameters. The authors consider different estimators for \(\psi\) and \(\lambda\) (including an iterative MLE algorithm) and five goodness-of-fit tests for this family: Kolmogorov, Kuiper, Cramér-von-Mises, Watson and Anderson-Darling. Symmetrization around the location parameter is proposed to derive more powerful tests. The critical values are derived for the tests via Monte-Carlo. The power of the tests is compared also via simulations. The conclusion is that the Kuiper test is most powerful against almost all alternative distributions (\(t\)-family, normal, beta, Weibull).
scientific article; zbMATH DE number 1878601