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Extreme value theory for singular measures
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2012In this paper, we perform an analytical and numerical study of the extreme values of specific observables of dynamical systems possessing an invariant singular measure. Such observables are expressed as functions of the distance of the orbit of initial conditions with respect to a given point of the attractor.
Faranda, Davide +3 more
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On the Rate of Convergence in Extreme Value Theory
Theory of Probability & Its Applications, 1989Let \(X_ 1,X_ 2,..\). be i.i.d. nonnegative random variables and \(M_ n=\max (X_ 1,...,X_ n)\). Further, let Y be a random variable with distribution belonging to one of the three Gnedenko extreme value types (say \(P(Y\leq x)=\exp (-1/x)\), \(x>0)\). Given a continuous, increasing function \(\Psi\) one can define the probability metrics \[ \rho_{\Psi}(
Omey, E., Rachev, S.
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The application of extreme value theory to pharmacometrics
Journal of Pharmacokinetics and Pharmacodynamics, 2020Clinical trials are often analyzed by examining the means, e.g., what is the mean treatment effect or what is the mean treatment difference, but there are times when analysis of the maximums (or minimums) are of interest. For instance, what is the highest heart rate that could be observed or what the smallest treatment effect that could be expected ...
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Penultimate Approximations in Extreme Value Theory
Extremes, 2000Let \(X_{n}, n\in N,\) be a sequence of independent, identically distributed r.v.'s with common distribution function \(F.\) In the recent paper by \textit{M. I. Gomes} and \textit{L. de Haan} [ibid. 2, No. 1, 71-85 (1999; Zbl 0947.60019)] exact penultimate approximation rates w.r.t.
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Practical Applications of the Theory of Extreme Values*
Journal of the American Statistical Association, 1955Abstract * A review article on Statistical Theory of Extreme Values and Some Practical Applications, by E. J. Gumbel, A Series of Lectures, National Bureau of Standards, Applied Mathematics Series, 33 (Washington, D. C.: U. S. Government Printing Office, 1954), and Probability Tables for the Analysis of Extreme-Value Data, National Bureau of Standards,
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Extreme value theory for stochastic processes.
Insurance: Mathematics and Economics, 1995This paper reviews Harald Cramer's work on extremes and crossings of stationary processes during the 1960's, and very briefly outlines some of the directions of later development of the probability...
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Extreme Value Theory: An Introduction
Technometrics, 2007George Michailidis, Stilian Stoev
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Extreme Value Theory and Value at Risk [PDF]
Value at Risk (VaR) is a measure of the maximum potential change in value of a portfolio of financial assets with a given probability over a given time horizon. VaR became a key measure of market risk since the Basle Committee stated that banks should be able to cover losses on their trading portfolios over a ten-day horizon, 99 percent of the time.
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“Extreme utilization” development theory of unconventional natural gas
Petroleum Exploration and Development, 2021Xinhua Ma
exaly

