In this paper, we give detailed descriptions of the Zero-Modified Negative Binomial distribution for analyzing count data. In particular, we study the characterizations and properties of this distribution, whose main advantage is its flexibility which makes it suitable for modeling a wide range of overdispersed and underdispersed count data (which may or may not be caused by zero-modification, i.e., the inflation or deflation of zeroes), without requiring previous knowledge about any of these inherent data characteristics. We derive maximum likelihood estimation of the model parameters based on positive observations, and evaluate the loss of efficiency by considering this procedure. We illustrate the suitability of this distribution on real data sets with different types of zero-modification.

在本文中，我们详细描述了用于分析计数数据的零修正负二项分布。特别是，我们研究了这种分布的特征和属性，其主要优点是其灵活性，使其适用于对各种过度分散和欠分散的计数数据进行建模（这可能是也可能不是由零修改引起的，即零的膨胀或紧缩），而无需事先了解任何这些固有数据特征。我们基于积极的观察得出模型参数的最大似然估计，并通过考虑这个过程来评估效率的损失。我们说明了这种分布在具有不同类型零修改的真实数据集上的适用性。