Extreme Value Distributions: An Overview of Estimation and Simulation

Abstract

The generalized extreme value distribution (GEVD) and various extreme value distributions are commonly applied in air pollution, telecommunications, operational risk management, finance, insurance, material sciences, economics, and hydrology, among many other industries that deal with extreme events. Extreme value distributions (EVDs) typically limit the distribution of maximum and minimum values for many random observations drawn from the same arbitrary distribution. Besides that, it is a crucial method for forecasting future events and emerged as critical method for predicting future events. As a result, prior research is required to select the best estimation method to obtain a reliable value for the parameters of extreme value distributions. This study provides an overview of three-parameter estimation methods based on goodness-of-fit statistics and root mean square error (RMSE). This paper reviewed and compared three estimation methods used to approximate values of parameters for simulated observations taken from the EVD and GEVD. The method of moments (MOMs), maximum likelihood estimator (MLE), and maximum product of spacing (MPS) were the methods investigated in this study. Our findings indicated that the MPS performed better based on the mean square errors (MSEs); meanwhile, the MPS had similar goodness-of-fit statistic values compared to the MLE.

Capacity in University Food Services: A Simulation Analysis Based on the case of Universidad Católica del Maule

“…Hence, this work has introduced the GEV distribution as a useful tool to strategically plan food service operations in terms of the likelihood that an overcapacity event occurs. In this regard, the authors suggest Abdulali et al (2022) which reviews the use of the GEV distribution in application scenarios.…”

Characteristics of Extreme Rainfall Events over Uganda during September to November Rainfall Season

“…The GEV distribution is designed to capture the characteristics of extreme events, making it a valuable tool for estimating and predicting extreme values . As a crucial method for analyzing extreme events, GEV distributions serve as a model that constrains the distribution of both maximum and minimum values derived from random observations drawn from the same arbitrary distribution (Abdulali et al, 2022). In this study, the GEV distribution model was employed to estimate extreme rainfall and its parameters.…”

Beyond Accuracy: Building Trustworthy Extreme Events Predictions Through Explainable Machine Learning

“…The second stage consists in using a classifier to train the predictions obtained through the first approach and classify the prediction probability of each value based on the preestablished labels for each event and evaluate the final result based on the goodness of matching and the quality of matched predictions. The two most popular distributions studied in the Extreme Value Theory EVT (Abdulali et al 2022) were considered. Namely, the Generalized Extreme Value (governs the distribution of its block maxima) and Generalized Pareto distributions (concerned with the distribution of excess values over a certain threshold) (Abdulali et al 2022;Castro-Camilo, Huser, and Rue 2022;De Zea Bermudez and Kotz 2010;Galib et al 2022).…”