The Bayesian Confidence Interval for Coefficient of Variation of Zero-inflated Poisson Distribution with Application to Daily COVID-19 Deaths in Thailand

Abstract

Coronavirus disease 2019 (COVID-19) has spread rapidly throughout the world and has caused millions of deaths. However, the number of daily COVID-19 deaths in Thailand has been low with most daily records showing zero deaths, thereby making them fit a Zero-Inflated Poisson (ZIP) distribution. Herein, confidence intervals for the Coefficient Of Variation (CV) of a ZIP distribution are derived using four methods: the standard bootstrap (SB), percentile bootstrap (PB), Markov Chain Monte Carlo (MCMC), and the Bayesian-based highest posterior density (HPD), for which using the variance of the CV is unnecessary. We applied the methods to both simulated data and data on the number of daily COVID-19 deaths in Thailand. Both sets of results show that the SB, MCMC, and HPD methods performed better than PB for most cases in terms of coverage probability and average length. Overall, the HPD method is recommended for constructing the confidence interval for the CV of a ZIP distribution. Doi: 10.28991/esj-2021-SPER-05 Full Text: PDF

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

“…Moreover, Srisuradetchai et al [18] proposed the profile-likelihood-based confidence interval for the geometric parameter of a ZIG distribution. Junnumtuam et al [19] constructed Wald confidence intervals for the parameters of a ZIP model; in an analysis of the number of daily COVID-19 deaths in Thailand using six models: Poisson, NB, geometric, Gaussian, ZIP, and ZINB, they found that the Wald confidence intervals for the ZIP model were the most suitable. Furthermore, Srisuradetchai et al [20] proposed three confidence intervals: a Wald confidence interval and score confidence intervals using the profile and the expected or observed Fisher information for the Poisson parameter in a ZIP distribution; the latter two outperformed the Wald confidence interval in terms of coverage probability, average length, and the coverage per unit length.…”