Exploring the realm of extreme weather events is indispensable for various engineering disciplines and plays a pivotal role in understanding climate change phenomena. In this study, we examine the ability of 10 probability distribution functions—including exponential, normal, two- and three-parameter log-normal, gamma, Gumbel, log-Gumbel, Pearson type III, log-Pearson type III, and SQRT-ET max distributions—to assess annual maximum 24 h rainfall series obtained over a long period (1972–2022) from three nearby meteorological stations. Goodness-of-fit analyses including Kolmogorov–Smirnov and chi-square tests reveal the inadequacy of exponential and normal distributions in capturing the complexity of the data sets. Subsequent frequency analysis and multi-criteria assessment enable us to discern optimal functions for various scenarios, including hydraulic engineering and sediment yield estimation. Notably, the log-Gumbel and three-parameter log-normal distributions exhibit superior performance for high return periods, while the Gumbel and three-parameter log-normal distributions excel for lower return periods. However, caution is advised regarding the overuse of log-Gumbel, due to its high sensitivity. Moreover, as our study considers the application of mathematical and statistical methods for the detection of extreme events, it also provides insights into climate change indicators, highlighting trends in the probability distribution of annual maximum 24 h rainfall. As a novelty in the field of functional analysis, the log-Gumbel distribution with a finite sample size is utilised for the assessment of extreme events, for which no previous work seems to have been conducted. These findings offer critical perspectives on extreme rainfall modelling and the impacts of climate change, enabling informed decision making for sustainable development and resilience.

El aprendizaje basado en problemas (ABP) es un método de enseñanza que se utiliza cada vez más en la enseñanza técnica. Tanto en la enseñanza de la ingeniería como en la de la arquitectura, el ABP se ha evaluado y ha demostrado su eficacia para mejorar el rendimiento académico de los estudiantes. La necesidad de trabajar en grupo y la limitación del número de alumnos por sesión de ABP requieren el uso de técnicas estadísticas robustas en la evaluación estadística correspondiente. En el presente trabajo se aplicaron dos pruebas estadísticas robustas: la prueba de la mediana y la prueba de Wilcoxon-Mann-Whitney (WMW). Utilizando una muestra de 35 estudiantes del Máster en Ingeniería Industrial de la Universidad de Huelva, distribuidos en tres cursos académicos (2021-22, 2022-23 y 2023-24), se aplicaron dichas pruebas en relación con el rendimiento académico. Hubo un grupo experimental (19 alumnos) y un grupo control (16 alumnos). Se han aclarado los detalles de la aplicación de cada prueba, incluyendo las hipótesis nula y alternativa, los estadísticos respectivos de cada prueba, y se ha resuelto el caso utilizando R. Se demuestra que existe una diferencia significativa en el aprendizaje entre el grupo experimental y el grupo de control, basándose en las pruebas de la mediana y de Wilcoxon-Mann-Whitney (WMW).Problem Based Learning (PBL) is a teaching method that is increasingly being used in technical education. In both engineering and architecture education, PBL has been evaluated and shown to be effective in improving students' academic performance. The need to work in groups and the limitation of the number of students per PBL session require the use of robust statistical techniques in the corresponding statistical evaluation. In the present work, two robust statistical tests were applied: the median test and the Wilcoxon-Mann-Whitney (WMW) test. Using a sample of 35 students of the Master in Industrial Engineering at the University of Huelva, distributed over three academic years (2021-22, 2022-23 and 2023-24), the said tests were applied in relation to academic performance. There was an experimental group (19 students) and a control group (16 students). The details of the application of each test have been clarified, including the null and alternative hypotheses, the respective statistics of each test, and the case has been solved using R. It is shown that there is a significant difference in learning between the experimental group and the control group, based on median and Wilcoxon-Mann-Whitney (WMW) tests.

Hydrometeorological models for hydraulic design rely on probability functions to model extreme rainfall. This study compares Log-Gumbel and Log-Pearson III functions using data from Almodóvar reservoir (Cádiz). Log-Gumbel, a variation of the Gumbel distribution, yields higher, safer estimates for long return periods (T), but is highly sensitive to data changes. Log-Pearson III, widely used and more stable, shows consistent results despite data variability. For designs with limited or variable data—common in hydraulic works—Log-Pearson III is preferred. However, for urban drainage where safety is prioritized over stability, Log-Gumbel offers a conservative alternative for high T values.