Testing Skew-Laplace Distribution Using Density-based Empirical Likelihood Approach

Abstract

Abstract. In this paper, we first describe the skew-Laplace distribution and its properties. We then introduce a goodness of fit test for this distribution according to the density-based empirical likelihood ratio concept. Asymptotic consistency of the proposed test is demonstrated. The critical values and Type I error of the test are obtained by Monte Carlo simulations. Moreover, the empirical distribution function (EDF) tests are considered for the skew-Laplace distribution to show they do not have acceptable Type I error in comparison with the proposed test. Results show that the proposed test has an excellent Type I error which does not depend on the unknown parameters. The results obtained from simulation studies designed to investigate the power of the test are presented, too. The applicability of the proposed test in practice is demonstrated by real data examples.

On transmuted skewed Laplace distribution and its application

“…The following are the probability density function, f(x) and the cumulative density function, F(x) of Skewed Laplace distribution by [2] .…”

“…The inability of the Laplace distribution to account for skewness led to the development of the skewed Laplace distribution. Therefore, the Laplace distribution was extended by adding skewness parameter which is used to model the skewness of the data [2] noted that in practical situations in which some skewness are presents, the Skew Laplace distribution is more flexible to model real data. The Skewed Laplace distribution has been used in Economics, Engineering, Finance and Biology.…”

A Density-Based Empirical Likelihood Ratio Approach for Goodness-of-fit Tests in Decreasing Densities

“…Then, the problem of developing an EL ratio-based test for the logistic distribution was investigated by Alizadeh Noughabi [1]. Following this, Safavinejad et al [21] investigated into the empirical likelihood approach for a goodness-of-fit test for special parametric null hypothesis of the skew-Laplace distribution against against the unknown alternative. A Monte Carlo simulation study was conducted to show that the proposed method preserve the type I error for the skew-Laplace distribution better than the empirical distribution function tests which are based on a measure of discrepancy between the empirical and hypothesized distributions.…”