Mohammadi Zohreh, Sajjadnia Zahra, Sharafi Maryam, Mamode Khan Naushad
Department of Statistics, Jahrom University, Persian Gulf Boulevard, Jahrom, Fars 7413188941 Iran.
Department of Statistics, Shiraz University, Adabiat Four Square, Shiraz, Fars 7145685464 Iran.
Iran J Sci Technol Trans A Sci. 2022;46(3):891-906. doi: 10.1007/s40995-022-01297-3. Epub 2022 May 23.
In this paper, we introduce a new stationary first-order integer-valued autoregressive process (INAR) with zero-and-one-inflated geometric innovations that is useful for modeling medical practical data. Basic probabilistic and statistical properties of the model are discussed. Conditional least squares and maximum likelihood estimators are proposed to estimate the model parameters. The performance of the estimation methods is assessed by some Monte Carlo simulation experiments. The zero-and-one-inflated INAR process is subsequently applied to analyze two medical series that include the number of new COVID-19-infected series from Barbados and Poliomyelitis data. The proposed model is compared with other popular competing zero-inflated and zero-and-one-inflated INAR models on the basis of some goodness-of-fit statistics and selection criteria, where it shows to provide better fitting and hence can be considered as another important commendable model in the class of INAR models.
在本文中，我们介绍了一种新的平稳一阶整值自回归过程（INAR），其创新项为零膨胀和一膨胀几何分布，该过程可用于对医学实际数据进行建模。讨论了该模型的基本概率和统计特性。提出了条件最小二乘估计和最大似然估计来估计模型参数。通过一些蒙特卡罗模拟实验评估了估计方法的性能。随后，将零膨胀和一膨胀INAR过程应用于分析两个医学序列，其中包括来自巴巴多斯的新冠病毒新感染序列数量和小儿麻痹症数据。在一些拟合优度统计量和选择标准的基础上，将所提出的模型与其他流行的竞争零膨胀和零一膨胀INAR模型进行了比较，结果表明该模型提供了更好的拟合，因此可被视为INAR模型类中的另一个重要且值得称赞的模型。
