This paper proposes a new generalized linear model with fractional binomial distribution. Zero-inflated Poisson/negative binomial distributions are used for count data that has many zeros. To analyze the association of such a count variable with covariates, zero-inflated Poisson/negative binomial regression models are widely used. In this work, we develop a regression model with the fractional binomial distribution that can serve as an additional tool for modeling the count response variable with covariates. Data analysis results show that on some occasions, our model outperforms the existing zero-inflated regression models.

翻译：本文提出了一种基于分数二项分布的新型广义线性模型。针对含有大量零值的计数数据，通常采用零膨胀泊松/负二项分布进行分析。为研究此类计数变量与协变量之间的关联，零膨胀泊松/负二项回归模型已被广泛使用。本研究开发了一种基于分数二项分布的回归模型，为含协变量的计数响应变量建模提供了新的工具。数据分析结果表明，在某些情况下，本模型性能优于现有的零膨胀回归模型。