On an approximation of function and its derivatives.
J. Prasad (1972)
Publications de l'Institut Mathématique [Elektronische Ressource]
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J. Prasad (1972)
Publications de l'Institut Mathématique [Elektronische Ressource]
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Fernando Cobos (1988)
Colloquium Mathematicae
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P. L. Papini (1987)
Matematički Vesnik
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Jiři Močkoř (1975)
Colloquium Mathematicae
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Jean Diebolt, Armelle Guillou, Rym Worms (2010)
ESAIM: Probability and Statistics
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The P.O.T. (Peaks-Over-Threshold) approach consists of using the Generalized Pareto Distribution (GPD) to approximate the distribution of excesses over a threshold. We use the probability-weighted moments to estimate the parameters of the approximating distribution. We study the asymptotic behaviour of these estimators (in particular their asymptotic bias) and also the functional bias of the GPD as an estimate of the distribution function of the excesses. We adapt penultimate approximation...
Stéphane Lozier, Damien Roy (2012)
Acta Arithmetica
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Jorge M. Arevalillo (2001)
Kybernetika
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The classical quantile approximation for the sample mean, based on the central limit theorem, has been proved to fail when the sample size is small and we approach the tail of the distribution. In this paper we will develop a second order approximation formula for the quantile which improves the classical one under heavy tails underlying distributions, and performs very accurately in the upper tail of the distribution even for relatively small samples.
R. B. Saxena (1962)
Annales Polonici Mathematici
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