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Heavy-tailed distributions and rating

by J. Beirlant, G. Matthys, G. Dierckx - ASTIN Bulletin , 2001
"... In this paper we consider the problem raised in the Astin Bulletin (1999) by Prof. Benktander at the occasion of his 80th birthday concerning the choice of an appropriate claim size distribution in connection with reinsurance rating problems. Appropriate models for large claim distributions play a c ..."
Abstract - Cited by 5 (0 self) - Add to MetaCart
in the tails and in more central portions of the claim distribution. To this end we propose a parametric model, termed the generalised Burr-gamma distribution, which possesses such flexibility. Throughout we consider a Norwegian fire insurance portfolio data set in order to illustrate the concepts. A small

Heavy–Tailed Distributions

by Cristian Meza, Felipe Osorio, O De La Cruz
"... Nonlinear mixed–effects models are very useful to analyze repeated measures data and are used in a variety of applications. Normal distributions for random effects and residual errors are usually assumed, but such assumptions make inferences vulnerable to the presence of outliers. In this work, we i ..."
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introduce an extension of a normal nonlinear mixed–effects model considering a subclass of elliptical contoured distributions for both random effects and residual errors. This elliptical subclass, the scale mixtures of normal (SMN) distributions, includes heavy–tailed multivariate distributions

Random Number Generators and Heavy-Tail Distributions

by Dror G. Feitelson
"... The mean and standard deviation of heavy-tailed distributions are often innite, as a result of non-negligible probabilities of sampling very high values. Generating random variates from such distributions may therefore depend on the range of output values of the underlying random number generator ..."
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The mean and standard deviation of heavy-tailed distributions are often innite, as a result of non-negligible probabilities of sampling very high values. Generating random variates from such distributions may therefore depend on the range of output values of the underlying random number

Heavy-Tailed Distributions in Combinatorial Search

by Carla Gomes, Bart Selman, Nuno Crato , 1997
"... Combinatorial search methods often exhibit a large variability in performance. We study the cost profiles of combinatorial search procedures. Our study reveals some intriguing properties of such cost profiles. The distributions are often characterized by very long tails or "heavy tails". W ..."
Abstract - Cited by 75 (14 self) - Add to MetaCart
. They are closely related to fractal phenomena, whose study was introduced by Mandelbrot. We believe this is the first finding of these distributions in a purely computational setting. We also show how random restarts can effectively eliminate heavy-tailed behavior, thereby dramatically improving the overall

1 Isoperimetry for product of heavy tails distributions

by Nathael Gozlan, Cyril Roberto, Paul-marie Samson
"... Extending an approach by Bobkov we obtain some isoperimetric inequalities for product of heavy tails distri-butions. ..."
Abstract - Cited by 1 (1 self) - Add to MetaCart
Extending an approach by Bobkov we obtain some isoperimetric inequalities for product of heavy tails distri-butions.

On Learning Mixtures of Heavy-Tailed Distributions

by Anirban Dasgupta, John Hopcroft, Jon Kleinberg, Mark Sandler , 2005
"... We consider the problem of learning mixtures of arbitrary symmetric distributions. We formulate sufficient separation conditions and present a learning algorithm with provable guarantees for mixtures of distributions that satisfy these separation conditions. Our bounds are independent of the varianc ..."
Abstract - Cited by 23 (2 self) - Add to MetaCart
We consider the problem of learning mixtures of arbitrary symmetric distributions. We formulate sufficient separation conditions and present a learning algorithm with provable guarantees for mixtures of distributions that satisfy these separation conditions. Our bounds are independent

An Example of a Heavy Tailed Distribution

by Norman Giraldo Gómez , 2005
"... Abstract We study some properties of the distribution function of a random variable of the form X = C D , where C and D are independent random variables. We assume that C is absolutely continuous and limited to a finite interval, such that its probability density function has definite limits at the ..."
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at the endpoints of the interval and D is exponentially distributed. We show that the tail functionF (.) := 1 − F (·) is of regular variation and that the distribution function F is asymptotically equivalent to a log-gamma distribution. Then F can be considered as a heavy tailed distribution. It is also shown

Numerical Methods for Analyzing Queues with Heavy-Tailed Distributions

by unknown authors
"... Keywords: Heavy-tailed distributions, numerical methods, Laplace transform inversion In many Internet-type queues, arrival and service distributions are heavy-tailed. A difficulty with analyzing these queues is that heavy-tailed distributions do not generally have closed-form Laplace transforms. A r ..."
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Keywords: Heavy-tailed distributions, numerical methods, Laplace transform inversion In many Internet-type queues, arrival and service distributions are heavy-tailed. A difficulty with analyzing these queues is that heavy-tailed distributions do not generally have closed-form Laplace transforms. A

On the estimation of the second order parameter for heavy-tailed distributions

by El Hadji Deme, Universite ́ Gaston Berger, Laurent Gardes , 2012
"... • The extreme-value index γ is an important parameter in extreme-value theory since it controls the first order behavior of the distribution tail. In the literature, numerous estimators of this parameter have been proposed especially in the case of heavy-tailed distributions, which is the situation ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
• The extreme-value index γ is an important parameter in extreme-value theory since it controls the first order behavior of the distribution tail. In the literature, numerous estimators of this parameter have been proposed especially in the case of heavy-tailed distributions, which is the situation

When Do Heavy-Tail Distributions Help?

by Nikolaus Hansen, Fabian Gemperle, Anne Auger, Petros Koumoutsakos
"... Abstract. We examine the evidence for the widespread belief that heavy tail distributions enhance the search for minima on multimodal objective functions. We analyze isotropic and anisotropic heavy-tail Cauchy distributions and investigate the probability to sample a better solution, depending on th ..."
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Abstract. We examine the evidence for the widespread belief that heavy tail distributions enhance the search for minima on multimodal objective functions. We analyze isotropic and anisotropic heavy-tail Cauchy distributions and investigate the probability to sample a better solution, depending
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