Abstract This study introduces the Poisson-Bilal distribution and its associated two models for modeling the over-dispersed count data sets. The Poisson-Bilal distribution has tractable properties and explicit forms for its statistical properties. A new over-dispersed count regression model and integer-valued autoregressive process with flexible innovation distribution are defined and studied comprehensively. Two real data sets are analyzed to prove empirically the importance of proposed models. Empirical findings show that the Poisson-Bilal distribution has important application fields in time series and regression modeling.

中文翻译：

---

具有关联回归和整数值自回归模型的新单参数离散分布

摘要 本研究介绍了 Poisson-Bilal 分布及其相关的两个模型，用于对过度分散的计数数据集进行建模。Poisson-Bilal 分布具有易于处理的特性和其统计特性的显式形式。定义并综合研究了一种新的过度分散计数回归模型和具有灵活创新分布的整数值自回归过程。分析了两个真实数据集，以凭经验证明所提出模型的重要性。实证结果表明，Poisson-Bilal 分布在时间序列和回归建模中具有重要的应用领域。