Distribution Pattern Analysis of Daily Confirmed COVID-19 Cases Across Selected Countries and Indian Epidemic Waves
DOI:
https://doi.org/10.6000/1929-6029.2026.15.25Keywords:
COVID-19, Distribution pattern analysis, Daily confirmed cases, Parametric distribution fitting, Skewness, Kurtosis, India epidemic waves, Public health statisticsAbstract
Daily confirmed COVID-19 cases have shown highly heterogeneous epidemic trajectories across different countries. The timing of the outbreak, the intensity of spread, the peak size, the duration of waves, and the reporting pattern varied substantially from one country to another. Due to this heterogeneity, the statistical analysis of daily confirmed cases is important not only to describe the epidemic burden but also to understand how cases are distributed over time.
In this study, the distribution pattern of COVID-19 daily cases is analysed for six countries: India, the United States, Brazil, the United Kingdom, South Africa, and Japan. The daily confirmed COVID-19 case data are taken from the Our World in Data COVID-19 dataset. The study period is restricted to a common analytical window from 30 January 2020 to 20 February 2022. After preprocessing, 753 daily observations are obtained for each country. For cross-country comparison, daily cases per million population are used, while India-specific wave analysis is performed using raw daily confirmed case counts.
The analysis evaluates descriptive distributional behaviour and parametric distribution fitting using selected candidate distributions, including Gamma, Generalised Gamma, Weibull, Log-Normal, Log-Logistic, Inverse Gaussian, Exponential, and Normal distributions. The results show that daily COVID-19 case distributions are right-skewed in all selected countries. The mean value is greater than the median value in all countries, showing that high-incidence days strongly affect the average case count. Country-wise distribution fitting shows that no single distribution is best for all countries. Log-Logistic distribution is selected for India, the United States and Japan; Inverse Gaussian distribution for Brazil; Generalised Gamma distribution for South Africa; and Log-Normal distribution for the United Kingdom.
For India, the wave-wise analysis shows that the three epidemic waves have different distributional behaviour. Wave 1 is best approximated by the Weibull distribution, Wave 2 by the Log-Normal distribution, and Wave 3 by the Generalised Gamma distribution. These findings indicate that COVID-19 daily case patterns are asymmetric, heterogeneous, and wave-specific. Hence, flexible positive-support and right-skewed distributions are more useful for describing the empirical distribution of positive daily confirmed COVID-19 cases than symmetric assumptions. However, the selected distributions are interpreted only as relative empirical approximations among the evaluated candidate distributions, and not as exact distributional laws of COVID-19 daily cases.
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