Extreme Value Distributions Overview

Extreme Value Distributions Overview - Extreme Value...

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Extreme Value Distributions EasyFit : select the best fitting distribution and use it to make better decisions. learn more The problem of modeling extreme or rare events arises in many areas where such events can have very negative consequences. Some examples of rare events include extreme floods and snowfalls, high wind speeds, extreme temperatures, large fluctuations in exchange rates, and market crashes. To develop appropriate probabilistic models and assess the risks caused by these events, business analysts and engineers frequently use the extreme value distributions (EVD). Contents Extreme Value Theory Gumbel Distribution (EVD Type I) Fréchet Distribution (EVD Type II) Weibull Distribution (EVD Type III) Generalized Extreme Value Distribution Using Extreme Value Distributions in EasyFit Extreme Value Theory Extreme value theory is a separate branch of statistics that deals with extreme events. This theory is based on the extremal types theorem , also called the three types theorem , stating that there are only three types of distributions that are needed to model the maximum or minimum of the collection of random observations from the same distribution. In other words, if you generate N data sets from the same distribution, and create a new data set that includes the maximum values from these N data sets, the resulting data set can only be described by one of the three models - specifically, the Gumbel , Fréchet , and Weibull distributions. These models, along with the Generalized Extreme Value distribution, are widely used in risk management, finance, insurance, economics, hydrology, material sciences, telecommunications, and many other industries dealing with extreme events. top
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Gumbel Distribution One of the first scientists to apply the theory was a German mathematician Emil Gumbel (1891-1966). Gumbel's focus was primarily on applications of extreme value theory to engineering problems, in particular modeling of meteorological phenomena such as annual flood flows: "It seems that the rivers know the theory. It only remains to convince the engineers of the validity of this
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This note was uploaded on 02/15/2012 for the course GEO 6938 taught by Professor Staff during the Summer '08 term at University of Florida.

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Extreme Value Distributions Overview - Extreme Value...

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