eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 2019-12-10 7 6 224 230 10.12691/ajams-7-6-4 AJAMS2019764 article Bachioua Lahcene drbachioua@gmail.com 1 Department of Basic Sciences, Prep. Year, P.O. Box 2440, University of Hail, Hail, Saudi Arabia In this article, the Normal Inverse Gaussian Distribution model (NIGDM) is extended to a new Extended Normal Inverse Gaussian Distribution (ENIGDM) and its derivate models find many applications. The author proposes a new model ENIGDM, which generalizes the models of normal inverse Gaussian distribution. This class of ENIGDM is to approximate an unknown risk-neutral density. The paper discusses different properties of the ENIGDM. In particular, the applicability of this new general model with five parameters is well justified by more results which represent mixtures of inverse Gaussian distributions. Then a discussion is begun of the potential of the normal inverse Gaussian distribution and Lévy’s process for modeling and analyzing statistical data, with a particular reference to extensive sets of observations and applications in wide varieties. http://pubs.sciepub.com/ajams/7/6/4/ajams-7-6-4.pdf Normal-Inverse Gaussian distribution generating and Quantile functions goodness-of-fit characteristics function survival function mixtures