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

Abstract

The Laplace distribution can be compared against the normal distribution. The Laplace distribution has an unusual, symmetric shape with a sharp peak and tails that are longer than the tails of a normal distribution. It has recently become quite popular in modeling financial variables (Brownian Laplace motion) like stock returns because of the greater tails. The Laplace distribution is very extensively reviewed in the monograph (Kotz et al. in the laplace distribution and generalizations—a revisit with applications 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 statistic is constructed based on the approach proposed by Vexler and Gurevich (Comput Stat Data Anal 54:531–545, 2010). In order to compute the test statistic, parameters of the Laplace distribution are estimated by the maximum likelihood method. Critical values and 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 carried out. Finally, two illustrative examples are presented and analyzed.

Keywords

Likelihood ratio / Laplace distribution / Density-based empirical likelihood ratio / Goodness-of-fit test / Monte Carlo simulation / Power study