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

Daouda Traoré; Issouf Traoré

doi:10.5281/zenodo.22157181

Authors

Daouda Traoré Laboratoire de Mathématiques Informatique et Applications
Issouf Traoré Laboratoire de Mathématiques Informatique et Applications

DOI:

https://doi.org/10.5281/zenodo.22157181

Keywords:

Stochastic comparisons, majorization, Weibull distribution, generalized Beta-Weibull distribution, COVID-19 Burkina Faso

Abstract

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 ? = 10.92) and that the Centre region (Ouagadougou) concentrates the highest peaks (? 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 ? and ?) 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.

Author Biographies

Daouda Traoré, Laboratoire de Mathématiques Informatique et Applications

Laboratoire de Mathématiques Informatique et Applications (LaMIA), Université Nazi BONI, 01 BP 1091 Bobo-Dioulasso 01, Burkina Faso.

Issouf Traoré, Laboratoire de Mathématiques Informatique et Applications

Laboratoire de Mathématiques Informatique et Applications (LaMIA), Université Nazi BONI, 01 BP 1091 Bobo-Dioulasso 01, Burkina Faso.

References

Shaked, M., Shanthikumar, J.G. (2007). Stochastic Orders. New York: Springer.

Bhakta, R., Balakrishnan, N., Kayal, S., Pradhan, S. (2024). Stochastic comparison results between two finite mixture models with generalized Weibull distributed components. Statistics, 58(3), 552-575.

Panahi, A.H., Jafari, H., Kia, G.S. (2024). Ordering properties of parallel and series systems with a general lifetime family of distributions for independent components under random shocks. Communications in Statistics: Theory and Methods, 53(21), 7582-7603.

Alshanbari, H.M., Almetwally, E.M., El-Bagoury, A.A.H. (2022). Novel Type I Half Logistic Burr-Weibull Distribution: Application to COVID-19 Data. Journal of Mathematics, 2022, 1444859.

Al-jabbar, A., Kelkinnama, M., Mahmoodi, S. (2025). Stochastic comparisons of extremes with a generalization of Weibull distribution. Statistics, 59(5), 1139-1160.

Marshall, A.W., Olkin, I., Arnold, B.C. (2011). Inequalities: Theory of Majorization and Its Applications. 2nd ed. New York: Springer.

McCool, J. (2012). Using the Weibull Distribution: Reliability, Modeling, and Inference. Hoboken: John Wiley & Sons.

Cordeiro, G.M., de Castro, M. (2011). A new family of generalized distributions. Journal of Statistical Computation and Simulation, 81(7), 883-898.

Balakrishnan, N., Zhao, P. (2013). Ordering properties of order statistics from heterogeneous populations: a review with an emphasis on some recent developments. Probability in the Engineering and Informational Sciences, 27(4), 403-443.

Belzunce, F., Martínez-Riquelme, C., Mulero, J. (2016). An Introduction to Stochastic Orders. London: Academic Press.

Li, H., Li, X. (2013). Stochastic Orders in Reliability and Risk. New York: Springer.

Denuit, M., Mesfioui, M. (2019). On the likelihood ratio order for extreme order statistics. Journal of Multivariate Analysis, 172, 145-158.

Müller, A., Stoyan, D. (2002). Comparison Methods for Stochastic Models and Risks. Chichester: Wiley.

Kirakoya-Samadoulougou, F., De Brouwere, V., Fokam, A.F., Ouédraogo, M., Yé, Y. (2022). Assessing the effect of seasonal malaria chemoprevention on malaria burden among children under 5 years in Burkina Faso. Malaria Journal, 21, 143.