Abstract

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.

中文翻译：

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离散拉普拉斯分布的参数估计

摘要

在本文中，我们考虑了离散拉普拉斯分布参数\（p \）的两个估计量之间的比较。推导了一种新的矩估计器（MME），并通过经典的Delta方法证明了其分布的渐近正态性。将新的MME与已知的最大似然估计器（MLE）进行比较。请注意，之前尚未研究过MLE的准确性属性。理论上并使用蒙特卡洛模拟研究对两个估计量的准确性和渐近正态性进行了研究。我们表明，MLE比MME具有更好的准确性。