Test of fit for Cauchy distribution based on the empirical likelihood ratio with application to the stock market price

Recently, it has been shown that the density based empirical likelihood concept extends and standardizes these methods, presenting a powerful approach for approximating optimal parametric likelihood ratio test statistics. In this article, we propose a density based empirical like- lihood goodness of t test for the Cauchy distribution. The properties of the test statistic are stated and the critical points are obtained. Power comparisons of the proposed test with some known competing tests are carried out via simulations. Our study shows that the proposed test is superior to the competitors in most of the considered cases and can con- dently apply in practice. Finally, a nancial data set is presented and analyzed.