Bayesian Inference for a New Negative Binomial-Samade Model for Time Series Data Counts with Its Properties and Applications

A new distribution was developed that mixed the negative binomial (NB) and Samade distributions, called the negative binomial-Samade (NB-SA) distribution. The properties of this distribution were studied, and the newly created distribution was applied using the framework of generalized linear models to build a time series data count model. The characteristics of overdispersion and heavy-tailed distribution of the count response variables were applied in the actual dataset modeling. Distribution parameters and the regression coefficient were estimated using a Bayesian approach. Results showed that the NB-SA model had significantly the highest efficiency compared with the classical NB and Poisson models for analyzing factors influencing the daily number of COVID-19 deaths in Thailand.