A Test for Skewness Within the Univariate and Multivariate Epsilon Skew Laplace Distributions

• Activity Number: 569
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Howraa Al-Mousawi*+ and Hassan Elsalloukh
• Companies: University of Arkansas at Little Rock and University of Arkansas at Little Rock
• Keywords: Epsilon skew Laplace distribution ; Measure of skewness ; Multivariate distributions ; heavy tail distributions

Abstract

In the univariate case, the popular measures of skewness ß_1 and kurtosis ß_2 have been proved to be useful measures in developing a test for normality and investigating the robustness of the standard normal theory procedures. While in the multivariate case, we have a p-dimensional skewness vector ß_12 introduced by Mardia in 1970, as multivariate skewness measure. In this work, the skewness measure has been derived for the Multivariate Epsilon Skew Laplace Distribution (MESL), the MESL is the multivariate version of the Epsilon Skew Laplace distribution (ESL) that have been introduce recently by Elsalloukh 2008. The MESL is an asymmetric distribution that can handle both symmetric, asymmetric, and heavy tail data. The p-dimensional skewness vector is introduced by using the Mardia's measures of skewness. Moreover, we provide a test for goodness of fit test to pick distributions that can fit the data correctly. We provide theoretical proofs and a Monte carlo simulation study to compare the ESL distributions to normal and skew normal distributions, in the univariate cases when modeling data.