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Heavytailed 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 Burrgamma 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
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 loggamma distribution. Then F can be considered as a heavy tailed distribution. It is also shown
1 Isoperimetry for product of heavy tails distributions
"... Extending an approach by Bobkov we obtain some isoperimetric inequalities for product of heavy tails distributions. ..."
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Extending an approach by Bobkov we obtain some isoperimetric inequalities for product of heavy tails distributions.
HeavyTailed 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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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
Random Number Generators and HeavyTail Distributions
"... The mean and standard deviation of heavytailed distributions are often innite, as a result of nonnegligible 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 heavytailed distributions are often innite, as a result of nonnegligible 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
Comparing downside risk measures for heavy tailed distributions
 Economic Letters
, 2006
"... Using regular variation to define heavy tailed distributions, we show that prominent downside risk measures produce similar and consistent ranking of heavy tailed risk. Thus regardless of the particular risk measure being used, assets will be ranked in a similar and consistent manner for heavy tai ..."
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Cited by 3 (2 self)
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Using regular variation to define heavy tailed distributions, we show that prominent downside risk measures produce similar and consistent ranking of heavy tailed risk. Thus regardless of the particular risk measure being used, assets will be ranked in a similar and consistent manner for heavy
On Learning Mixtures of HeavyTailed 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
Control Chart for Autocorrelated Processes with Heavy Tailed Distributions
"... Abstract: Standard control charts are constructed under the assumption that the observations taken from the process of interest are independent over time; however, in practice the observations in many cases are actually correlated. This paper considers the problem of monitoring a process in which ..."
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Cited by 2 (1 self)
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the observations can be represented as a firstorder autoregressive model following a heavy tailed distribution. We propose a chart based on computing the control limits using the process mean and the standard error of the least absolute deviation for the case when the process quality characteristics follows a
Control Chart for Heavy Tailed Distributions
, 2007
"... ABSTRACT Standard control charts with control limits determined by the mean and standard error of the mean are constructed based on the assumption that the distribution of the quality characteristic being monitored follows a normal distribution. However, this assumption is not always valid. It is p ..."
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Cited by 1 (1 self)
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. It is proposed to use a chart based on computing the control limits using the process mean and the standard error of the least absolute deviation for the case where the process quality characteristics follow a heavy tailed t distribution. Such a control chart is more effective than the normal distribution based
Results 1  10
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