Bayesian Computation for the Parameters of a Zero-Inflated Cosine Geometric Distribution with Application to COVID-19 Pandemic Data

A new three-parameter discrete distribution called the zero-inflated cosine geometric (ZICG) distribution is proposed for the first time herein. It can be used to analyze over-dispersed count data with excess zeros. The basic statistical properties of the new distribution, such as the moment generating function, mean, and variance are presented. Furthermore, confidence intervals are constructed by using the Wald, Bayesian, and highest posterior density (HPD) methods to estimate the true confidence intervals for the parameters of the ZICG distribution. Their efficacies were investigated by using both simulation and real-world data comprising the number of daily COVID-19 positive cases at the Olympic Games in Tokyo 2020. The results show that the HPD interval performed better than the other methods in terms of coverage probability and average length in most cases studied.