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Heavy-tailed distributions and rating
- 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 ..."
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Cited by 5 (0 self)
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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
"... 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
"... 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
, 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 ..."
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Cited by 75 (14 self)
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. 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
"... Extending an approach by Bobkov we obtain some isoperimetric inequalities for product of heavy tails distri-butions. ..."
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Cited by 1 (1 self)
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Extending an approach by Bobkov we obtain some isoperimetric inequalities for product of heavy tails distri-butions.
On Learning Mixtures of Heavy-Tailed Distributions
, 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 ..."
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Cited by 23 (2 self)
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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
, 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
"... 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
, 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 ..."
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Cited by 1 (0 self)
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• 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?
"... 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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Cited by 8 (2 self)
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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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