Modified Method of Moments for Generalized Laplace Distributions

Abstract

In this short note, we demonstrate the failure of the classic method of moments for parameter estimation of symmetric variance-gamma (generalized Laplace) distributions. This disproves the claim found in the literature that method of moments works well for generalized asymmetric Laplace distributions and related models. We use both theoretical analysis (multivariate delta method) and simulations to make our case. Finally, we modify the method of moments by taking absolute moments to improve efficiency.