In this article, we conduct a further analysis of the Epsilon skew Laplace (ESL) distribution introduced by Elsalloukh [4]. The ESL distribution is used to fit asymmetric data as an alternative to the Laplace and normal distributions. It can also be used in Economics, Engineering, Finance, and Biology. In particular, we provide estimation for the ESL parameters using two methods, the Maximum Likelihood Estimators (MLE) method and the moment estimators method. We also derive the moment generating and the characteristic functions of the ESL along with some properties.

skew distribution, asymmetric distribution, skew Laplace distribution, epsilon skew Laplace, asymmetric Laplace.