The paper discusses very general extensions to existing inflation models for discrete random variables, allowing an arbitrary set of points in the sample space to be either inflated or deflated relative to a baseline distribution. The term flation is introduced to cover either inflation or deflation of counts. Examples include one-inflated count models where the baseline distribution is zero-truncated and count models for data with a few unusual large values. The main result is that inference about the baseline distribution can be based solely on the truncated distribution which arises when the entire set of flation points is truncated. A major application of this result relates to estimating the size of a hidden target population, and examples are provided to illustrate our findings.

中文翻译：

---

计数数据的一般平坦模型

该论文讨论了对离散随机变量的现有膨胀模型的非常普遍的扩展，允许样本空间中的任意一组点相对于基线分布膨胀或收缩。引入术语扁平化以涵盖计数的通货膨胀或紧缩。示例包括单膨胀计数模型，其中基线分布被零截断，以及用于具有一些不寻常的大值的数据的计数模型。主要结果是，关于基线分布的推断可以仅基于截断分布，当整组平坦点被截断时出现截断分布。该结果的一个主要应用涉及估计隐藏目标人群的规模，并提供了示例来说明我们的发现。