A Study on Max Domain of Attraction Condition of Fréchet Distribution with Case Study
Article Sidebar
-
Domain of Attraction Condition, Fréchet Distribution, Norming Constant, P-P Plot, Q-Q Plot, Return Level Plot
Abstract
Extreme value theory (EVT) refers to a 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 behavior 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 fExtremes and ismev for parameter estimation and diagnostic plots.
Full text article
References
[1]-X. Liu, “Data analysis in extreme value theory,” Dep. Stat. Oper. Res. Univ. North Carolina Chapel Hill, 2009.
[2]-S. Coles, J. Bawa, L. Trenner, and P. Dorazio, An introduction to statistical modeling of extreme values, vol. 208. Springer, 2001:P37,P49.
[3]-R. A. Fisher and L. H. C. Tippett, “Limiting forms of the frequency distribution of the largest or smallest member of a sample,” in Mathematical Proceedings of the Cambridge Philosophical Society, 1928, vol. 24, no. 2, pp. 180–190.
[4]-R. Von Mises, “Über allgemeine Quadraturformeln.,” J. für die reine und Angew. Math., vol. 174, pp. 56–67, 1936.
[5]-B. Gnedenko, “Sur la distribution limite du terme maximum d’une serie aleatoire,” Ann. Math., pp. 423–453, 1943.
[6]-L. De Haan and A. Ferreira, Extreme value theory: an introduction. Springer Science & Business Media, 2007:PP17-21.
[7]-K. Abbas and T. Yincai, “Comparison of Estimation Methods for Frechet Distribution with Known Shape.,” Casp. J. Appl. Sci. Res., vol. 1, no. 10, 2012.
[8]-J. Beirlant, Y. Goegebeur, J. Segers, and J. L. Teugels, Statistics of extremes: theory and applications.John Wiley & Sons, 2006:PP56-59.
[9]-E. Omey, F. Mallor, and E. Nualart, “An introduction to statistical modelling of extreme values. Application to calculate extreme wind speeds,” 2009.
[10]-E. Castillo, A. S. Hadi, N. Balakrishnan, and J.-M. Sarabia, Extreme value and related models with applications in engineering and science. Wiley Hoboken, NJ, 2005:P108,P148.
[11]-S. Kotz and S. Nadarajah, Extreme value distributions: theory and applications. World Scientific, 2000:PP210-213.
Authors
This work is licensed under a Creative Commons Attribution 4.0 International License.
In a brief statement, the rights relate to the publication and distribution of research published in the journal of the University of Sebha where authors who have published their articles in the journal of the university of Sebha should how they can use or distribute their articles. They reserve all their rights to the published works, such as (but not limited to) the following rights:
- Copyright and other property rights related to the article, such as patent rights.
- Research published in the journal of the University of Sebha and used in its future works, including lectures and books, the right to reproduce articles for their own purposes, and the right to self-archive their articles.
- The right to enter a separate article, or for a non-exclusive distribution of their article with an acknowledgment of its initial publication in the journal of Sebha University.
Privacy Statement The names and e-mail addresses entered on the Sabha University Journal site will be used for the aforementioned purposes only and for which they were used.