STOCHASTIC COMPARISONS OF EXTREMES FOR GENERALIZED WEIBULL AND BETA-WEIBULL DISTRIBUTIONS: SIMULATION AND APPLICATION TO COVID-19 IN BURKINA FASO

Comparing the intensity of epidemic waves across regions or time periods is a major public health decision-making issue. This article addresses this problem by developing a theoretical framework for stochastically comparing extremes (minimums and maximums) of random variables following generalized Weibull and Beta-Weibull distributions. The approach relies on vector majorization to rank parameter dispersion and on stochastic orders to compare peaks and troughs of epidemic waves. The established theorems are validated by numerical simulations. An application to daily COVID-19 data from Burkina Faso (13 regions, March 2020 – March 2022) is carried out. The results show that wave 2 (December 2020 – February 2021) was the most intense (mean θ = 10.92) and that the Centre region (Ouagadougou) concentrates the highest peaks (θ reaching 77.9). The generalized Beta-Weibull model provides a better fit than the classical Weibull model, but its estimation is fragile (saturation of parameter a at 100). The comparison theorems are validated for the Weibull model (5 out of 6 pairs). The matrix chain majorization analysis (simultaneous comparison of θ and γ) shows that no wave satisfies the required conditions, which in itself is an epidemiological finding: the intensity and shape of regional peaks are independent. Limitations include the disparity in the number of adjusted regions across waves and the low activity of wave 1. The study opens perspectives for the analysis of other infectious diseases (malaria, meningitis) and for extension to other countries in the West African subregion.