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490 – Advances in Statistical Software
A Test for Skewness Within the Univariate and Multivariate Epsilon Skew Laplace Distributions
Howraa Al Mousawi
Arkansas Department of Health
Jose Guardiola
Texas A&M University
Hassan Elsalloukh
University of Arkansas at Little Rock
In the univariate case, the popular measures of skewness, and kurtosis, 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, 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 and 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 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.