In this paper, a zero-and-one-inflated Poisson (ZOIP) regression model is proposed. The maximum likelihood estimation (MLE) and Bayesian estimation for this model are investigated. Three estimation methods of the ZOIP regression model are obtained based on data augmentation method which is expectation-maximization (EM) algorithm, generalized expectation-maximization (GEM) algorithm and Gibbs sampling respectively. A simulation study is conducted to assess the performance of the proposed estimation for various sample sizes. Finally, an accidental deaths data set is analyzed to illustrate the practicability of the proposed method.

中文翻译：

---

零加一膨胀泊松回归模型

在本文中，提出了零和一膨胀泊松（ZOIP）回归模型。研究了该模型的最大似然估计 (MLE) 和贝叶斯估计。基于数据增强方法得到了ZOIP回归模型的三种估计方法，分别是期望最大化(EM)算法、广义期望最大化(GEM)算法和Gibbs采样。进行模拟研究以评估针对各种样本大小的建议估计的性能。最后，分析了一个意外死亡数据集，以说明所提出方法的实用性。