Statistical Methods for Testing the Coefficient of Variation of the Daily Number of COVID-19 Deaths in Thailand

Abstract

Coronavirus disease (COVID-19) has been classified as a pandemic by the World Health Organization (WHO). It was initially detected in Wuhan City, China, in 2019 and has since spread to every other country. It caused many deaths, and the number of infections became greater than 184.68 million as of 5 July 2021. The daily number of COVID-19 deaths fits a gamma distribution, and this led us to consider testing this via the coefficient of variation (CV) of these data. Herein, we present four statistical methods for testing the CV of a gamma population based on the Score method using maximum likelihood estimation (MLE), the Score method using new moment estimation (NME), the Wald method using MLE, and the Wald method using NME. To compare their performances, a simulation study was conducted with many shape parameter value variations for a gamma distribution. The performances of the test statistics were compared based on their empirical type I error rates and powers of the test. The simulation results show that the test statistics based on the Wald method performed better than the ones based on the Score method in terms of the attained nominal significance level. The Score and Wald methods using NME were more efficient than those using MLE when sample sizes were small whereas those using MLE performed better than with NME for large sample sizes. Furthermore, the efficacies of the proposed methods were illustrated by applying them to the daily number of COVID-19 deaths in Thailand.