Parameter estimation for Discrete Laplace Distribution

In this paper, we consider a comparison between two estimators of the parameter $p$ of the discrete Laplace distribution. A new method of moments estimator (MME) is derived and the asymptotic normality of its distribution is proven by applying the classical Delta method. The new MME is compared with the already known maximum likelihood estimator (MLE). Note that no accuracy properties of the MLE have been investigated before. The accuracy and the asymptotic normality of both estimators are investigated theoretically and using Monte Carlo simulation studies. We show that the MLE possesses better accuracy properties than the MME