Comparison between VG-levy and Kernel function estimation with application

In this article, we present the variance Gamma Levy model that was obtained from the Brownian motion Gamma with their parameter estimation methods (Maximum Likelihood (MLE) and method of moments (MME)). Then, we compare them with Kernel density function depending on MASE. Our application concerned with the Apple company that is listed on the Nasdaq, their data are suitable for the VG-Levy model and achieved the proper conditions of Levy of stability and independence, which means that Apple company was efficient in providing the information to investors.