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 decisionmaking issue. This article addresses this problem by developing a theoretical framework for stochasticallycomparing extremes (minimums and maximums) of random variables following generalized Weibull andBeta-Weibull distributions. The approach relies on vector majorization to rank parameter dispersion and onstochastic orders to compare peaks and troughs of epidemic waves. The established theorems are validatedby numerical simulations. An application to daily COVID-19 data from Burkina Faso (13 regions, March2020 – March 2022) is carried out. The results show that wave 2 (December 2020 – February 2021) was themost intense (mean θ = 10.92) and that the Centre region (Ouagadougou) concentrates the highest peaks (θreaching 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 forthe Weibull model (5 out of 6 pairs). The matrix chain majorization analysis (simultaneous comparison ofθ 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 ofadjusted regions across waves and the low activity of wave 1. The study opens perspectives for the analysisof other infectious diseases (malaria, meningitis) and for extension to other countries in the West Africansubregion.