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Statistics of Multivariate Extremes
International Statistical Review / Revue Internationale de Statistique, 1990Summary: The paper is concerned with statistical aspects of multivariate extreme value distributions. The family is infinite dimensional, so direct parametric estimation is not possible. We describe such nonparametric and parametric approaches, the latter being based on parametric subfamilies.
Smith, R. L., Tawn, J. A., Yuen, H. K.
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2004
We use in the following the theory developed in the preceding chapters to discuss a few nonstandard applications. Of interest are here the statistical estimation of the cluster distribution and of the extremal index in a stationary situation.
Beirlant, J. +3 more
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We use in the following the theory developed in the preceding chapters to discuss a few nonstandard applications. Of interest are here the statistical estimation of the cluster distribution and of the extremal index in a stationary situation.
Beirlant, J. +3 more
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Annual Review of Statistics and Its Application, 2015
Statistics of extremes concerns inference for rare events. Often the events have never yet been observed, and their probabilities must therefore be estimated by extrapolation of tail models fitted to available data. Because data concerning the event of interest may be very limited, efficient methods of inference play an important role.
Davison, Anthony C., Huser, Raphaël
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Statistics of extremes concerns inference for rare events. Often the events have never yet been observed, and their probabilities must therefore be estimated by extrapolation of tail models fitted to available data. Because data concerning the event of interest may be very limited, efficient methods of inference play an important role.
Davison, Anthony C., Huser, Raphaël
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On a Class of Extremal Problems in Statistics
Mathematische Operationsforschung und Statistik. Series Optimization, 1981Let m denote the infimum of the Integral of a function q w r t all probability measures with given marginals. The determination of m is of interest for a series of stochastic problems. In the present paper we prove a duality theorem for the determination of m and give some examples for its application.
Gaffke, N., Rüschendorf, L.
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Abstract We discuss in detail the statistics of the maximum and the minimum in our two principal models: IID random variables and the random walk model.
Satya N Majumdar, Grégory Schehr
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Satya N Majumdar, Grégory Schehr
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Dynamics and Statistics of Extreme Events
2010Complex dynamics is characterized by an irregular, non-periodic time dependence of characteristic quantities. Rare fluctuations which lead to unexpectedly large (or small) values are called extreme events. Since such large deviations from the system’s mean behavior have in many applications huge impact, their statistical characterization and their ...
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Statistical Decision for Bivariate Extremes
1989Bivariate extreme random pairs, with extreme margins, have for the distribution function, in the case of maxima, or for the survival function, in the case of minima, a dependence function. For the cases of Gumbel margins for maxima or of the exponential margins for minima an index of dependence as well the correlation coefficient are obtained ...
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