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

Sunisa Junnumtuam, Sa-Aat Niwitpong, Suparat Niwitpong


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


Bootstrap; Markov Chain Monte Carlo; Highest Posterior Density.


Valencia, Damian N. “Brief Review on COVID-19: The 2020 Pandemic Caused by SARS-CoV-2.” Cureus (March 24, 2020). doi:10.7759/cureus.7386.

Cameron, A. Colin, and Pravin K. Trivedi. “Regression analysis of count data.” Vol. 53. Cambridge University Press, (2013).

Lambert, Diane. “Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing.” Technometrics 34, no. 1 (February 1992): 1-14. doi:10.2307/1269547.

Böhning, D., E. Dietz, P. Schlattmann, L. Mendonça, and U. Kirchner. “The Zero-inflated Poisson Model and the Decayed, Missing and Filled Teeth Index in Dental Epidemiology.” Journal of the Royal Statistical Society: Series A (Statistics in Society) 162, no. 2 (January 1999): 195–209. doi:10.1111/1467-985x.00130.

Lee, Cheol-Eung, and Sang Kim. “Applicability of Zero-Inflated Models to Fit the Torrential Rainfall Count Data with Extra Zeros in South Korea.” Water 9, no. 2 (February 16, 2017): 123. doi:10.3390/w9020123.

Boucher, Jean-Philippe, Michel Denuit, and Montserrat Guillen. “Number of Accidents or Number of Claims? An Approach with Zero-Inflated Poisson Models for Panel Data.” Journal of Risk and Insurance 76, no. 4 (December 2009): 821–846. doi:10.1111/j.1539-6975.2009.01321.x.

Kusuma, Rahmaniar Dwinta, and Yogo Purwono. “Zero-Inflated Poisson Regression Analysis On Frequency Of Health Insurance Claim PT. XYZ.” Proceedings of the 12th International Conference on Business and Management Research (ICBMR 2018) (2019). doi:10.2991/icbmr-18.2019.52.

Rodrigues, Josemar. “Bayesian Analysis of Zero-Inflated Distributions.” Communications in Statistics - Theory and Methods 32, no. 2 (January 3, 2003): 281–289. doi:10.1081/sta-120018186.

Xu, Hai-yan, Min Xie, and Thong Ngee Goh. “Objective Bayes Analysis of Zero-Inflated Poisson Distribution with Application to Healthcare Data.” IIE Transactions 46, no. 8 (May 2014): 843–852. doi:10.1080/0740817x.2013.770190.

Unhapipat, Suntaree, Montip Tiensuwan, and Nabendu Pal. “Bayesian Predictive Inference for Zero-Inflated Poisson (ZIP) Distribution with Applications.” American Journal of Mathematical and Management Sciences 37, no. 1 (October 20, 2017): 66–79. doi:10.1080/01966324.2017.1380545.

Wagh, Yogita S., and Kirtee K. Kamalja. “Zero-Inflated Models and Estimation in Zero-Inflated Poisson Distribution.” Communications in Statistics-Simulation and Computation 47, no. 8 (August 4, 2017): 2248–2265. doi:10.1080/03610918.2017.1341526.

Srisuradetchai, P., and Junnumtuam, S. “Wald Confidence Intervals for the Parameter in a Bernoulli Component of Zero-Inflated Poisson and Zero-Altered Poisson Models with Different Link Functions” Science & Technology Asia 25, no.2 (2020) doi:10.14456/scitechasia.2020.16.

Waguespack, Dustin, K. Krishnamoorthy, and Meesook Lee. “Tests and Confidence Intervals for the Mean of a Zero-Inflated Poisson Distribution.” American Journal of Mathematical and Management Sciences 39, no. 4 (June 22, 2020): 383–390. doi:10.1080/01966324.2020.1777914.

Junnumtuam, Sunisa, Sa-Aat Niwitpong, and Suparat Niwitpong. “The Bayesian Confidence Interval for the Mean of the Zero-Inflated Poisson Distribution.” Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2020. Lecture Notes in Computer Science 12482. Springer, Cham. (November, 2020): 419–430. doi:10.1007/978-3-030-62509-2_35.

Zou, Y., Hannig, J., and Young, D.S. “Generalized fiducial inference on the mean of zero-inflated Poisson and Poisson hurdle models.” J Stat Distrib App 8, no.5 (2021) doi: 10.1186/s40488-021-00117-0.

Vangel, Mark G. “Confidence Intervals for a Normal Coefficient of Variation.” The American Statistician 50, no. 1 (February 1996): 21–26. doi:10.1080/00031305.1996.10473537.

Panichkitkosolkul, W. “A simulation comparison of new confidence intervals for the coefficient of variation of Poisson distribution.” Silpakorn University Science and Technology Journal 4, no. 2 (2010):14-20. doi:10.14456/sustj.2010.7.

Panichkitkosolkul, W. “Asymptotic confidence interval for the coefficient of variation of Poisson distribution: a simulation study.” Maejo International Journal of Science and Technology 4, no. 1 (2010): 1-7.

Niwitpong, Sa-aat. “Confidence Intervals for Coefficient of Variation of Lognormal Distribution with Restricted Parameter Space.” Applied Mathematical Sciences 7 (2013): 3805–3810. doi:10.12988/ams.2013.35251.

Yosboonruang, Noppadon, Suparat Niwitpong, and Sa-Aat Niwitpong. “Confidence Intervals for Coefficient of Variation of Three Parameters Delta-Lognormal Distribution.” Studies in Computational Intelligence (November 24, 2018): 352–363. doi:10.1007/978-3-030-04263-9_27.

Efron, B., and R. Tibshirani. “Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy.” Statistical Science 1, no. 1 (February 1, 1986): 54-75. doi:10.1214/ss/1177013815.

Tanner, Martin A., and Wing Hung Wong. "The calculation of posterior distributions by data augmentation." Journal of the American statistical Association 82, no. 398 (June, 1987): 528-540. doi:10.2307/2289457.

Chen, Ming-Hui, and Qi-Man Shao. “Monte Carlo Estimation of Bayesian Credible and HPD Intervals.” Journal of Computational and Graphical Statistics 8, no. 1 (March 1999): 69-92. doi:10.2307/1390921.

Box, George E.P., and George C. Tiao. “Bayesian Inference in Statistical Analysis”, New York, Wiley (April 6, 1992). doi:10.1002/9781118033197.

Full Text: PDF

DOI: 10.28991/esj-2021-SPER-05


  • There are currently no refbacks.

Copyright (c) 2021 Sunisa Sunisa Junnumtuam, Sa-Aat Niwitpong, Suparat Niwitpong