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	Extreme value theory - Wikipedia, the free encyclopedia
		Extreme value theory is a branch of statistics dealing with the extreme deviations from the median of probability distributions.
		Extreme value theory is important for assessing risk for highly unusual events, such as 100-year floods.
		Extreme value distributions are the limiting distributions for the minimum or the maximum of a very large collection of random observations from the same arbitrary distribution.
	en.wikipedia.org /wiki/Extreme_value_theory (399 words)

	Extreme value theory -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		Extreme value theory is a branch of (A branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parameters) statistics dealing with the extreme deviations from the median of (Click link for more info and facts about probability distribution) probability distributions.
		Extreme value theory is important for assessing (A venture undertaken without regard to possible loss or injury) risk for highly unusual events, such as (Click link for more info and facts about 100-year flood) 100-year floods.
		The field of extreme value theory was founded by the German mathematician, pacifist, and anti-Nazi campaigner (Click link for more info and facts about Emil Julius Gumbel) Emil Julius Gumbel who described the (Click link for more info and facts about Gumbel distribution) Gumbel distribution in the (The decade from 1950 to 1959) 1950s.
	www.absoluteastronomy.com /encyclopedia/E/Ex/Extreme_value_theory.htm (532 words)

	8.1.6.3. Extreme value distributions
		In the context of reliability modeling, extreme value distributions for the minimum are frequently encountered.
		The distribution often referred to as the Extreme Value Distribution (Type I) is the limiting distribution of the minimum of a large number of unbounded identically distributed random variables.
		The Weibull distribution and the extreme value distribution have a useful mathematical relationship.
	www.itl.nist.gov /div898/handbook/apr/section1/apr163.htm (648 words)

	Extreme value theory (Site not responding. Last check: 2007-11-07)
		Extreme value theory is an area of statistics devoted to the development of models and techniques for estimating the behaviour of unusual or rare events.
		The fundamental difficulty with estimating extreme values is the need to make inferences about levels of a process (the sea-level, say) for which there is little, or no, data.
		In the absence of physical or empirical rules for making such calculations, the usual approach is to develop models based on asymptotic theory - a kind of extreme value version of central limit theory - and there are a number of such models available.
	www.stats.bris.ac.uk /Postgrad/topics/coles.html (394 words)

	Extreme value - Wikipedia, the free encyclopedia
		The largest and the smallest element of a set are called extreme values, or extreme records.
		If an infinite chain S is bounded, then the closure Cl(S) of the set will have a minimum and a maximum, which are the greatest lower bound and the least upper bound of the set S, and which either belong to S or are accumulation points of S.
		See also: extreme value theorem, extreme value theory.
	en.wikipedia.org /wiki/Extreme_value (344 words)

	ABSTRACT: Hydrologic assessment: application of extreme value theory for climate extreme scenarios construction. (Site not responding. Last check: 2007-11-07)
		Extreme Value Theory (EVT) technique is proposed to simulate current and future climate extreme scenarios to be used for hydrologic impact models.
		The EVT is a branch of applied statistics which specifically deals with the facts of frequency increase of extreme events.
		The EVT offers to converge a series of maxima (minima) series of the meteorological data to the Generalized Extreme Value (GEV) distribution, to model the behaviour of the excess over a given threshold basing on the generalized Pareto distribution (GP) and to produce probabilistic statistics of climate extremes.
	cgrg.geog.uvic.ca /abstracts/GoldsteinHydrologic.html (311 words)

	Extreme value article - Extreme value record differentiable function stationary point partial order - What-Means.com (Site not responding. Last check: 2007-11-07)
		An extreme value or record is a maximum or minimum.
		For a differentiable function a necessary condition is that it is a stationary point.
		Extreme value article - Extreme value definition - what means Extreme value
	www.what-means.com /encyclopedia/Minimum (90 words)

	Extreme Value Theory (EVT) whitepaper
		Extreme Value Theory (EVT) is a branch of statistics that deals with such rare situations and that gives a scientific alternative to pure guesswork.
		EVT is the most scientific approach to a difficult problem: predicting the size of a rare event.
		EVT as well as any other model is only an abstraction of reality and not a silver bullet: no science can replace experience, domain knowledge and human intuition, as our work in risk management for the finance and corporate industry has shown us again and again.
	www.approximity.com /papers/evt_wp_html/evt_wp.html (1471 words)

	1994 Building Publications - Extreme Value Theory and Applications: Proceedings of the Conference on Extreme Value ... (Site not responding. Last check: 2007-11-07)
		Extreme Value Theory and Applications: Proceedings of the Conference on Extreme Value Theory and Applications.
		Extreme value theory has by now penetrated the social sciences, the medical profession, economics and even astronomy.
		To utilize and stimulate progress in the theory of extremes and promote its application, an international conference was organized in which equal weight was given to theory and practice.
	fire.nist.gov /bfrlpubs/build94/art059.html (262 words)

	Statistics of Weather and Climate Extremes
		This web page is intended to serve as a resource for the use of the statistical theory of extreme values in the analysis of weather and climate extremes and their impacts.
		In terms of the tail of a distribution, the corresponding theorem states that the observations exceeding a high threshold, under very general conditions, are approximately distributed as the generalized Pareto distribution [of which the exponential (light tail) and Pareto (heavy tail) are special cases].
		The modern approach to extreme value analysis is based on a point process representation, equivalent to: (i) a Poisson process governing the rate of occurrence of exceedance of a high threshold; and (ii) a generalized Pareto distribution for the excess over the threshold.
	www.isse.ucar.edu /extremevalues/extreme.html (939 words)

	Math: Extreme Value Theory
		If you have tried to learn extreme value theory (EVT) and been frustrated by all the arcane mathematics, Kotz and Nadarajah is the perfect solution.
		Extreme value theory (EVT) is the study of probabilistic extremes.
		For example, if you were to randomly draw 10,000 standard normal variates, the maximum of those values is a random variable.
	www.riskbook.com /topics/math_extreme_value_theory.htm (83 words)

	Steps in Applying Extreme Value Theory to Finance: A Review
		EVT is useful in modelling the impact of crashes or situations of extreme stress on investor portfolios.
		Contrary to value-at-risk approaches, EVT is used to model the behaviour of maxima or minima in a series (the tail of the distribution).
		However, implementation of EVT faces many challenges, including the scarcity of extreme data, determining whether the series is “fat-tailed,” choosing the threshold or beginning of the tail, and choosing the methods of estimating the parameters.
	www.ideas.uqam.ca /ideas/data/Papers/bcabocawp00-20.html (426 words)

	The Extreme Value Approach to VaR - An Introduction, Part 1, by Kevin Dowd
		None of these approaches comes to terms with the basic issue posed by extreme value estimation: that the estimation of low frequency events with limited data is highly problematic, and that these difficulties increase, as these events become rarer.
		The result is extreme value theory-a tailor-made approach to these problems that focuses on the distinctiveness of extreme values.
		The key to this approach is the extreme value theorem, which tells us what the asymptotic distribution of extreme values should look like.
	www.fenews.com /fen11/extreme.html (781 words)

	EXTREME VALUE THEORY FACTS AND INFORMATION (Site not responding. Last check: 2007-11-07)
		Extreme value theory is a branch of statistics dealing with the extreme deviations from the median of probability_distributions.
		# Most common at this moment is the tail-fitting approach based on the second theorem in extreme value theory (Theorem II Pickands (1975), Balkema and de Haan (1974)).
		The field of extreme value theory was founded by the German mathematician, pacifist, and anti-Nazi campaigner Emil Julius Gumbel who described the Gumbel_distribution in the 1950s.
	www.witwib.com /Extreme_value_theory (377 words)

	MATH 453: Extreme Value Theory
		This module aims to develop the asymptotic theory, and associated techniques for modelling and inference, associated with the analysis of extreme values of random processes.
		Classical theory and applications: data examples; the ‘three-types’ theorem; the generalized extreme value distribution; modelling annual maxima; model diagnostics.
		Multivariate extremes: asymptotic dependence and asymptotic independence; measures of dependence; empirical estimators; multivariate value models.
	www.lancs.ac.uk /users/acadreg/gcr/math453.htm (163 words)

	Amazon.com: Books: Extreme Value Theory in Engineering (Statistical Modeling and Decision Science) (Site not responding. Last check: 2007-11-07)
		Extreme value theory is very important in the analysis of floods, air pollution, reliability and many other data sources where the maximum or minimum of a sequence of observations is considered.
		Extensions of the asymptotic theory to correlated sequences were later developed by Berman for Gaussian sequences and Loynes, O'Brien, Leadbetter and others in the more general context of stationary sequences satisfying mixing conditions.
		They have been applied also to other fields where "extremes" in an intuitive sense exist, such as extreme accidents in car insurance (long chain collisions of cars in the fog, heights of waves in the ocean, etc.).
	www.amazon.com /exec/obidos/tg/detail/-/0121634752?v=glance (833 words)

	Amazon.com: Books: Extreme Value Distributions: Theory and Applications (Site not responding. Last check: 2007-11-07)
		Probabilistic extreme value theory is a curious and fascinating blend of an enormous variety of applications involving natural phenomena such as rainfall, floods, wind gusts, air pollution, and corrosion, and delicate advanced mathematical results on point processes and regularly varying functions.
		In chapter 2, which covers generalized extreme value distributions, the authors reference Castillo and Hadi (1997), but this reference is missing from the bibliography.
		The theory of extremes and related topics of outlier detection are near and dear to me. My Ph.D. thesis dealt with special stationary sequences and how Gnedenko's three type theorem extended from the i.i.d.
	www.amazon.com /exec/obidos/tg/detail/-/1860942245?v=glance (1168 words)

	Extreme value theory (Site not responding. Last check: 2007-11-07)
		Extreme waves, rainfall, and floods are of basic importance in oceanograpy and hydrology, as are high wind speeds and extreme temperatures in meteorology.
		The goals of the extreme value group are to develop new statistical and probabilistic methods for extremes and to use them in a wide range of applied problems.
		Methodological research includes general limit theory for upcrossings and maxima and for spatial extremes, clustering of random points in space, improved computation for maxima, statistical methods for non-homogeneous spatial extremes and stochastic volatility models for financial applications.
	www.math.chalmers.se /Stat/Research/extreme.html (307 words)

	CEPR Discussion Paper Abstracts
		In statistics, extremes of a random process refer to the lowest observation (the minimum) and to the highest observation (the maximum) over a given time-period.
		An approach based on extreme values to compute the VaR thus covers market conditions ranging from the usual environment considered by the existing VaR methods to the financial crises which are the focus of stress testing.
		Univariate extreme value theory is used to compute the VaR of a fully-aggregated position while multivariate extreme value theory is used to compute the VaR of a position decomposed on risk factors.
	www.cepr.org /pubs/new-dps/dplist.asp?dpno=2161 (306 words)

	Extreme Value Theory for Risk Managers - McNeil (ResearchIndex) (Site not responding. Last check: 2007-11-07)
		Abstract: We provide an overview of the role of extreme value theory (EVT) in risk management (RM), as a method for modelling and measuring extreme risks.
		The key point is that EVT gives the theory for describing extremes (maxima, minima, longest runs,...
		9 Pitfalls and opportunities in the use of extreme value theor..
	citeseer.ist.psu.edu /mcneil99extreme.html (458 words)

	Extreme value theory
		Extreme value theory is a branch of statistics dealing with the extreme deviations from the mean of statistical distributions[?].
		Extreme value theory group at Chalmers University (http://www.cs.chalmers.se/Stat/Research/researchgroups/extreme.html)
		Extreme value theory an empirical analysis of equity risk (http://citeseer.nj.nec.com/gavin00extreme.html)
	www.ebroadcast.com.au /lookup/encyclopedia/ex/Extreme_value_theory.html (123 words)

	[No title]
		Extreme Value Theory and Applications, Proceedings of the Conference on Extreme Value Theory and Applications, Volume I, Gaithersburg, Maryland 1993, Kluwer Academic Publishers, Boston, 1994.
		Extreme Value Theory and Applications, Proceedings of the Conference on Extreme Value Theory and Applications, Volume II, Gaithersburg, Maryland 1993, Journal of Research of the National Institute of Standards and Technology, Volume 99, No. 4, 1995.
		Extreme Value Theory and Applications, Proceedings of the Conference on Extreme Value Theory and Applications, Volume III, Gaithersburg, Maryland, 1993, NIST Special Publication 860, 1994.
	www.itl.nist.gov /div898/conf/evc.html (260 words)

	The Extreme Value Approach to VaR -- An Introduction, Part 4 by Kevin Dowd
		In particular, they flout statistical theory, which tells us what the distribution of extreme returns should look like, at least asymptotically.
		As one recent study concluded, "When the smoke clears, the contribution of EVT [EV theory] remains basic and useful: it helps us to draw smooth curves through the tails of empirical...
		EVT gives the best estimates of extreme events and represents the most honest approach to measuring the uncertainty inherent in the problem.
	www.fenews.com /fen13/extreme.html (679 words)

	Minimax Risk Bounds in Extreme Value Theory, Holger Drees
		Asymptotic minimax risk bounds for estimators of a positive extreme value index under zero-one loss are investigated in the classical i.i.d.
		To this end, we prove the weak convergence of suitable local experiments with Pareto distributions as center of localization to a white noise model, which was previously studied in the context of nonparametric local density estimation and regression.
		Ibragimov, I. and Khas'minskii, R. On nonparametric estimation of values of a linear functional in Gaussian white noise.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.aos/996986509 (438 words)

	Measuring Risk With Extreme Value Theory - Smith (ResearchIndex) (Site not responding. Last check: 2007-11-07)
		22 Extreme value analysis of environmental time series: An appl..
		2 ete des lois extremes multivariees et de la convergence de..
		Extreme Value Analysis Of Insurance Risk - Richard Smith (1999)
	citeseer.ist.psu.edu /269004.html (648 words)

	Extreme value theory, ergodic theory and the boundary between short memory and long memory for stationary stable ...
		Extreme value theory, ergodic theory and the boundary between short memory and long memory for stationary stable processes, Gennady Samorodnitsky
		Extreme value theory, ergodic theory and the boundary between short memory and long memory for stationary stable processes
		We observe a sharp change in the asymptotic behavior of the sequence of partial maxima as flow changes from being dissipative to being conservative, and argue that this may indicate a change from a short memory process to a long memory process.
	projecteuclid.org /Dienst/UI/1.0/Display/euclid.aop/1084884857 (207 words)

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