ABSTRACT

To model count data with excess zeros, ones and twos, for the first time we introduce a so-called zero-one-two-inflated Poisson (ZOTIP) distribution, including the zero-inflated Poisson (ZIP) and the zero-and-one-inflated Poisson (ZOIP) distributions as two special cases. We establish three equivalent stochastic representations for the ZOTIP random variable to develop important distributional properties of the ZOTIP distribution. The Fisher scoring and expectation–maximization (EM) algorithms are derived to obtain the maximum likelihood estimates of parameters of interest. Bootstrap confidence intervals are also provided. Testing hypotheses are considered, simulation studies are conducted, and two real data sets are used to illustrate the proposed methods.

摘要

为了对具有过多零、一和二的计数数据进行建模，我们首次引入了所谓的零一二膨胀泊松(ZOTIP) 分布，包括零膨胀泊松(ZIP) 和零与-单膨胀泊松(ZOIP) 分布作为两个特例。我们为 ZOTIP 随机变量建立了三个等效的随机表示，以开发 ZOTIP 分布的重要分布特性。Fisher 评分和期望最大化推导出 (EM) 算法以获得感兴趣参数的最大似然估计。还提供了 Bootstrap 置信区间。考虑了测试假设，进行了模拟研究，并使用两个真实数据集来说明所提出的方法。