Testing the validity of Cauchy model based on the informational energy

Abstract

In this article, a test statistic for testing the validity of the Cauchy model based on the informational energy is introduced. Consistency of our test is shown. Also, we show that the distribution of the test statistic does not depend on the location and scale parameters. Through a simulation study, we obtain the critical values of the test statistic and then the power of the test is computed by Monte Carlo method against different alternatives. The performance of the proposed test with some competing tests is compared. Our results show that our test is superior to the classical non-parametric tests and can apply to a testing problem in practice.