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190
Subexponential Distributions
, 1997
"... We survey the properties and uses of the class of subexponential probability distributions, paying particular attention to their use in modelling heavytailed data such as occurs in insurance and queueing applications. We give a detailed summary of the core theory and discuss subexponentiality in va ..."
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Cited by 38 (7 self)
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We survey the properties and uses of the class of subexponential probability distributions, paying particular attention to their use in modelling heavytailed data such as occurs in insurance and queueing applications. We give a detailed summary of the core theory and discuss subexponentiality
Resource Sharing with Subexponential Distributions
, 2002
"... We investigate the distribution of the waiting time V in an M/G/1 processor sharing queue with traffic intensity #<1. This queue represents a baseline model for evaluating efficient and fair network resource sharing algorithms, e.g. TCP flow control. When the distribution of job size B belongs t ..."
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Cited by 7 (1 self)
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to a class of subexponential distributions with tails heavier than e  , it is shown that as x P[V>x]=P[B>(1 #)x](1 + o(1)).
HAZARD RATES AND SUBEXPONENTIAL DISTRIBUTIONS
"... This paper is dedicated to the memory of Tatjana Ostrogorski and also to our coauthor Aleksandras Baltrunas who died during the preparation of this paper. Both were infinite dimensional mathematicians and both unfortunately died too young. Abstract. A distribution function F on the nonnegative half ..."
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Cited by 1 (0 self)
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halfline is called subexponential if limx→∞(1−F ∗n(x))/(1−F (x)) = n for all n 2. We obtain new sufficient conditions for subexponential distributions and related classes of distribution functions. Our results are formulated in terms of the hazard rate. We also analyze the rate of convergence
The rate of convergence for subexponential distributions
 Lith. Math. J
, 1998
"... Abstract. A distribution function F on the nonnegative real line is called subexponential if limx→∞(1−F ∗n(x))/(1−F(x)) = n for all n 2, where F ∗n denotes the nfold Stieltjes convolution of F with itself. In this paper, we consider the rate of convergence in the above definition and in its densit ..."
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Cited by 8 (1 self)
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Abstract. A distribution function F on the nonnegative real line is called subexponential if limx→∞(1−F ∗n(x))/(1−F(x)) = n for all n 2, where F ∗n denotes the nfold Stieltjes convolution of F with itself. In this paper, we consider the rate of convergence in the above definition and in its
Convolutions of longtailed and subexponential distributions
"... Convolutions of longtailed and subexponential distributions play a major role in the analysis of many stochastic systems. We study these convolutions, proving some important new results through a simple and coherent approach, and showing also that the standard properties of such convolutions follow ..."
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Cited by 4 (0 self)
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Convolutions of longtailed and subexponential distributions play a major role in the analysis of many stochastic systems. We study these convolutions, proving some important new results through a simple and coherent approach, and showing also that the standard properties of such convolutions
Telecommunication Traffic, Queueing Models, and Subexponential Distributions
, 1999
"... This article reviews various models within the queueing framework which have been suggested for teletraffic data. Such models aim to capture certain stylised features of the data, such as variability of arrival rates, heavytailedness of on and offperiods and longrange dependence in teletraffic t ..."
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Cited by 11 (1 self)
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transmission. Subexponential distributions constitute a large class of heavytailed distributions, and we investigate their (sometimes disastrous) influence within teletraffic models. We demonstrate some of the above effects in an explorative data analysis of Munich Universities' intranet data.
Subexponential Distributions  Large Deviations with Applications to Insurance and Queueing Models
"... We present a ne large deviations theory for heavytailed distributions whose tails are heavier than exp( t) and have nite second moment. Asymptotics for rst passage times are derived. The results are applied to estimate the nite time ruin probabilities in insurance as well as the busy peri ..."
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Cited by 5 (0 self)
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We present a ne large deviations theory for heavytailed distributions whose tails are heavier than exp( t) and have nite second moment. Asymptotics for rst passage times are derived. The results are applied to estimate the nite time ruin probabilities in insurance as well as the busy
Simulating Gi/gi/1 Queues And Insurance Risk Processes With Subexponential Distributions
"... This paper deals with estimating small tail probabilities of the steadystate waiting time in a GI/GI/1 queue with heavytailed (subexponential) service times. The problem of estimating infinite horizon ruin probabilities in insurance risk processes with heavytailed claims can be transformed into t ..."
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been confined to M/GI/1 queueing systems. The general approach is to use the PollaczekKhintchine transformation to transform the problem into that of estimating the tail distribution of a geometric sum of independent subexponential random variables. However, no such useful transformation exists when
Results 1  10
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190