Satheesh Kumar C, Ramachandran Rakhi
Department of Statistics, University of Kerala, Thiruvananthapuram, India.
J Appl Stat. 2019 Jul 24;47(3):506-523. doi: 10.1080/02664763.2019.1645098. eCollection 2020.
Count data with excess zeros are so common in several areas of scientific research. In particular, the zero-inflated version of count data models has been used for modelling data sets with excessive number of zeros. In this regard, zero-inflated Poisson distribution has received much attention in the literature. Through this paper, we propose a generalized class of zero-inflated Poisson distribution namely 'zero-inflated Hermite distribution (ZIHD)', which can be considered as a more flexible class of zero-inflated Poisson-type distribution suitable for tackling overdispersed data sets. Here we investigate several important properties of the ZIHD along with a discussion on certain inference aspects of the model. Certain test procedures for checking zero-inflation have also been developed and these tests have been investigated by using simulation studies. Further, two real life data applications are given for illustrating the usefulness of the model.
在多个科学研究领域中，带有过多零值的计数数据非常常见。特别是，计数数据模型的零膨胀版本已被用于对具有过多零值的数据集进行建模。在这方面，零膨胀泊松分布在文献中受到了广泛关注。通过本文，我们提出了一类广义的零膨胀泊松分布，即“零膨胀埃尔米特分布（ZIHD）”，它可被视为一类更灵活的零膨胀泊松型分布，适用于处理过度分散的数据集。在此，我们研究了ZIHD的几个重要性质，并对该模型的某些推断方面进行了讨论。还开发了一些用于检验零膨胀的测试程序，并通过模拟研究对这些测试进行了研究。此外，给出了两个实际数据应用案例来说明该模型的实用性。
