Empirical Likelihood Ratio-Based Goodness-of-Fit Test for the Laplace Distribution

The Laplace distribution can be compared against the normal distribution.The Laplace distribution has an unusual,symmetric shape with a sharp peak and tailsthat are longer than the tails of a normal distribution.It has recently become quitepopular in modeling financial variables(Brownian Laplace motion)like stock returnsbecause of the greater tails.The Laplace distribution is very extensively reviewed in themonograph(Kotz et al.in the laplace distribution and generalizations-a revisit withapplications to communications,economics,engineering,and finance.Birkhauser,Boston,2001).In this article,we propose a density-based empirical likelihood ratio(DBELR)goodness-of-fit test statistic for the Laplace distribution.The test statisticis constructed based on the approach proposed by Vexler and Gurevich(Comput StatData Anal 54:531-545,2010).In order to compute the test statistic,parameters of theLaplace distribution are estimated by the maximum likelihood method.Critical valuesand power values of the proposed test are obtained by Monte Carlo simulations.Also,power comparisons of the proposed test with some known competing tests are carriedout.Finally,two illustrative examples are presented and analyzed.