Generalized Pareto distribution applied to the analysis of maximum rainfall events in Uruguaiana, RS, Brazil

Abstract

The rainfall monitoring allows us to understand the hydrological cycle that not only influences the ecological and environmental dynamics, but also affects the economic and social activities. These sectors are greatly affected when rainfall occurs in amounts greater than the average, called extreme event; moreover, statistical methodologies based on the mean occurrence of these events are inadequate to analyze these extreme events. The Extreme Values Theory provides adequate theoretical models for this type of event; therefore, the Generalized Pareto Distribution (Henceforth GPD) is used to analyze the extreme events that exceed a threshold. The present work has applied both the GPD and its nested version, the Exponential Distribution, in monthly rainfall data from the city of Uruguaiana, in the state of Rio Grande do Sul in Brazil, which calculates the return levels and probabilities for some events of practical interest. To support the results, the goodness of fit criteria is used, and a Monte Carlo simulation procedure is proposed to detect the true probability distribution in each month analyzed. The results show that the GPD and Exponential Distribution fits to the data in all months. Through the simulation study, we perceive that the GPD is more suitable in the months of September and November. However, in January, March, April, and August the, Exponential Distribution is more appropriate, and in the other months, we can use either one.

Best-fit probability distribution models for monthly rainfall of Northeastern Brazil

“…Also, high variability was observed among the p-values. In agreement with these results, Martins et al (2020) observed that the GP distribution showed good fits to rainfall data for the Uruguaiana region (Southern Brazil). Their results showed adequate GP distribution fits the data in all months.…”

“…The goodness of fit tools indicated that although no distribution provides the best fit to the data for all months, the three-parameter lognormal distribution shows a generally better fit than the other distributions. Martins et al (2020) applied both the Generalized Pareto Distribution (GP) and the Exponential Distribution (ED), in monthly rainfall data from the city of Uruguaiana, in the state of Rio Grande do Sul. The results show that the GP and ED fit the data in all months.…”

Intensive Computational Method Applied for Assessing Specialty Coffees by Trained and Untrained Consumers

“…It should be noted that if H 0 is rejected, it can be said that the data are independent. In both tests, the significance level of 1% was adopted [25].…”

The assessment of annual rainfall field by applying different interpolation methods in the state of Rio Grande do Sul, Brazil

“…The analysis of climatic variables essentially consists of two stages: an exploratory one, using descriptive statistics in order to verify the normality of the data and to discard the need for transformation in the set and also to identify the existence of possible outliers; and the second, which is based on the adjustment of mathematical statistical models to the data, which can study the phenomena with different approaches, as well as the occurrence of extreme values [5][6][7], temporal distribution (Pereira Britto, Barletta and Mendonça [8]), spatial distribution [9], intensity of the phenomenon [10], among others.…”