Abstract

We consider two classes of exponential dispersion models of discrete probability distributions which are defined by specifying their variance functions in their mean value parameterization. These classes were considered in our earlier paper as models of overdispersed zero-inflated distributions. In this paper we analyze the application of these classes to fit count data having overdispersed and zero-inflated statistics. For this reason, we first elaborate on the computational aspects of the probability distributions, before we consider the data fitting with our models. We execute an extensive comparison with other statistical models that are recently proposed, on both real data sets, and simulated data sets. Our findings are that our framework is a flexible tool that gives excellent results in a wide range of cases. Moreover, specifically when the data characteristics show also large skewness and kurtosis our models perform best.

摘要

我们考虑两类离散概率分布的指数离散模型，它们是通过在平均值参数化中指定其方差函数来定义的。在我们之前的论文中，这些类别被视为过度分散的零膨胀分布的模型。在本文中，我们分析了这些类在拟合具有过度分散和零膨胀统计数据的计数数据中的应用。因此，在考虑数据与模型的拟合之前，我们首先详细阐述概率分布的计算方面。我们在真实数据集和模拟数据集上与最近提出的其他统计模型进行了广泛的比较。我们的发现是，我们的框架是一个灵活的工具，可以在各种情况下提供出色的结果。而且，