Numerical Experiments on Extreme Event Predictions Using Fisher–Tippett Model

The Fisher–Tippett distribution, also known as the Extreme Value Type I distribution, represents one of the fundamental models in extreme value theory. It is primarily used for modeling the distribution of the maximum (or minimum) of a large collection of random variables, making it an essential tool in engineering, finance, hydrology, and environmental sciences. This proposal aims to investigate the statistical properties, parameter estimation methods, and practical applications of the Fisher–Tippett distribution through both theoretical and numerical approaches. The distribution’s probability density function (PDF) and cumulative distribution function (CDF) will be derived and interpreted for real-world datasets where extreme values govern system behavior. This study presents two numerical examples: first, modeling yearly maximum river flow to assess flood risk, and second, examining extreme stress values in structural materials. Parameter estimation will be done using maximum likelihood estimation (MLE) and the method of moments, and then validated with goodness-of-fit tests. The results should show how well Fisher-Tippett modeling captures the statistical behavior of extreme events. Also, comparisons with other extreme value distributions will show its strengths and weaknesses. This work gives a clear method for using the Fisher-Tippett distribution to various scientific problems, giving information on prediction, risk management, and decision-making when things are uncertain. The outcomes help create strong statistical models for forecasting extreme events, which is key to dealing with global issues like climate change, infrastructure durability, and financial risk.