A study on max domain of attraction condition of Fréchet distribution with case study
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Domain of Attraction Condition, Fréchet Distribution, Norming Constant, P-P Plot, Q-Q Plot, Return Level Plot.
Abstract
Extreme value theory (EVT) refers to branch of statistics that deals with extreme events (minimum or maximum). In EVT, Fréchet distribution is one of the most important to model extreme events. In this paper, the first objective is to discuss the problem which is called the domain of attraction condition of maximum belonging to the domain of Fréchet distribution by using Gnedenko's, von Mises, Castillo and de Hann necessary and sufficient condition. The second objective, graphical methods are used to detect an appropriate distribution. The third objective of the present study is to model the behaviour of annual maximum wind speed data at Albany, and Hartford by using Fréchet distribution. The distribution parameters will be estimated by Maximum Likelihood Estimation (MLE). The results show that the two applications are significant to be fitted by Fréchet model. All computations in this work are performed by R programming with packages of fExtreme and ismev for parameter estimation and diagnostic plots.
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