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Unformatted text preview: Generalized extreme value Probability density function Cumulative distribution function Parameters location (real) scale (real) shape (real) Support Probability density function (pdf) where Cumulative distribution function (cdf) Mean where g k = (1 k ) Median Generalized extreme value distribution From Wikipedia, the free encyclopedia (Redirected from Extreme value distribution) In probability theory and statistics, the generalized extreme value distribution (GEV) is a family of continuous probability distributions developed within extreme value theory to combine the Gumbel, Frchet and Weibull families also known as type I, II and III extreme value distributions. Its importance arises from the fact that it is the limit distribution of the maxima of a sequence of independent and identically distributed random variables. Because of this, the GEV is used as an approximation to model the maxima of long (finite) sequences of random variables. Contents 1 Specification 2 Mean, standard deviation, mode, skewness and kurtosis excess 3 Link to Frchet, Weibull and Gumbel families 4 Extremal types theorem 5 References Specification Your continued donations keep Wikipedia running! Generalized extreme value distribution - Wikipedia... http://en.wikipedia.org/wiki/Extreme_value_distri... 1 of 5 08/09/2008 09:48 Mode Variance Skewness Excess kurtosis Entropy Moment- generating function (mgf) Characteristic function The generalized extreme value distribution has cumulative distribution function for 1 + ( x ) / > 0 , where is the location parameter, > 0 the scale parameter and the shape parameter. The density function is, consequently again, for 1 + ( x ) / > 0 ....
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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.
- Summer '08