Ridge and Broken Adaptive Ridge estimators for a new zero-inflated Poisson-Garima model

Our concern in this paper is that we first present the zero-inflated Poisson-Garima (ZIPG) distribution and then we propose a model based on this distribution. The ZIPG distribution as well as the ZIPG model are both used to work on count data (CD) sets with a very high proportion of zeros. Such data is often referred to scientifically as zero-inflated (ZI) data. To be more specific, in this work we will first recall the general formula and important properties of the Poisson-Garima (PG) distribution, and then we provide a general formula for the ZIPG distribution as well as its model. The relevant formulas for parameter estimation through maximum likelihood estimation (MLE) algorithm are also presented in this study. Because the MLE has many limitations, we introduce two more methods that have more advantages than the traditional MLE, which are Ridge and Broken Adaptive Ridge (BAR) estimators. To test the performance of the ZIPG model, we conducted several simulation investigations and analysis of an actual data set. The results obtained in this paper show that the proposed model is very meaningful in practice and helps readers to have more tools to analyze data.