Comparative efficiency of Wald, Score, and Variance Stabilizing Confidence Intervals for the Coefficient of Variation of a Poisson Distribution: A Monte Carlo Study with Application to Nigeria's 2026 Lassa Fever Outbreak.

Author

Okafor Joseph Iweanandu, Ashinze Akudo M, Kerry Chinedu. C


Abstract

 The coefficient of variation (CV) is a popular, unit free measure of relative dispersion, and interval estimation of the CV for Poisson distributed count data has received growing attention. 

This work assesses three confidence interval (CI) construction methods for the coefficient of variation (CV) of a Poisson distribution. The Three methods considered are Wald method, Score method, and Variance Stabilizing (VS) method. Each derived by first constructing a confidence interval for the Poisson mean and transforming to the relation  K=1μ. A Monte Carlo simulation (20,000 replications per case) assessed coverage probability and expected interval length across true means μ= (1, 2, 5, 10, 20, 50) and sample sizes n=(10, 20, 30, 50, 100). Results show that while all three methods approach nominal 95% coverage as n and μ increase, the Wald interval is markedly unstable for small means and small samples (μ = 1, n = 10), showing both under coverage and a mean interval length several times larger than the Score and VS alternatives. Score and VS intervals maintain coverage closer to nominal levels with substantially shorter average widths throughout the parameter space considered, the three methods were then applied to a real, publicly reported dataset: weekly national counts of newly confirmed Lassa fever cases in Nigeria during the ongoing 2026 outbreak. In this application, all three methods produced closely agreeing intervals because the observed weekly mean was large enough to be outside the unstable region identified in simulation, however, the empirical sample CV (0.758) substantially exceeded the CV implied by the fitted Poisson mean (0.176), indicating pronounced over dispersion relative to the Poisson assumption, a finding with direct implications for outbreak monitoring applications of this methodology. Recommendations for specialist and guidance for additional research are discussed.



Keywords

coefficient of variation, confidence interval, Poisson distribution, coverage probability, Monte Carlo simulation, Lassa fever, Nigeria



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References


  • Barker, L. (2002). A comparison of nine confidence intervals for a Poisson parameter when the                  
    • expected number of events is ≤5. American Statistician, 56, 85–89.
  • Junnumtuam, S., Niwitpong, S.-A., & Niwitpong, S. (2021). The Bayesian confidence interval for
    • coefficient of variation of zero-inflated Poisson distribution with application to daily COVID-19 deaths in Thailand. Emerging Science Journal, 5, 62–76.
  • Nigeria Centre for Disease Control and Prevention(NCDC), 2026. Lassa fever situation reports,
  • News Agency of Nigeria(NAN), (2026) NCDC weekly Lassa fevercase updates, epidemiological
    • weeks6, 7, 18, 19, 25, 26, 27, 28, 30, 2026.
  • Panichkitkosolkul, W. (2010). Asymptotic confidence interval for the coefficient of variation of
    • Poisson distribution: A simulation study. Maejo International Journal of Science and Technology, 4 (1), 1–7.
  • Panichkitkosolkul, W. (2013). A simulation comparison of new confidence intervals for the coefficient
    • of variation of a Poisson distribution. Science, Engineering and Health Studies, 4 (2), 14–20.
  • Pearson, K. (1896). Mathematical contributions to the theory of evolution. III. Regression, heredity,
    • and pan ixia. Philosophical Transactions of the Royal Society A, 187, 253–318.
  • Vangel, M. G. (1996). Confidence intervals for a normal coefficient of variation. The American
    • Statistician, 50 (1), 21–26.

 

 

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