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Cumulative broadband network traac is often thought to be well modelled by fractional Brownian motion. However, some traac measurements do not show an agreement with the Gaussian marginal distribution assumption. We show that if connection rates are modest relative to heavy tailed connection length distribution tails, then stable L evy motion is a sensible(More)
The copula of a multivariate distribution is the distribution transformed so that one dimensional marginal distributions are uniform. We review a different transformation of a multivariate distribution which yields standard Pareto for the marginal distributions and the resulting distribution we call the Pareto copula. Use of the Pareto copula has a certain(More)
Huge data sets from the teletraac industry exhibit many non-standard characteristics such as heavy tails and long range dependence. Various estimation methods for heavy tailed time series with positive innovations are reviewed. These include parameterestimation and model identiicationmethods for autoregressionsand moving averages. Parameter estimation(More)
We study the time it takes until a a uid queue with a nite, but large, holding capacity reaches the overrow point. The queue is fed by an on/oo process, with a heavy tailed on distribution, which is known to have long memory. It turns out that the expected time until overrow, as a function of capacity L, increases only polynomially fast, and so overrows(More)
Second order regular variation is a reenement of the concept of regular variation which is useful for studying rates of convergence in extreme value theory and asymptotic normality of tail estimators. For a distribution tail 1 ? F which possesses second order regular variation, we discuss how this property is inherited by 1 ? F 2 and 1 ? F 2. We also(More)
We develop a framework for regularly varying measures on complete separable metric spaces S with a closed cone C removed, extending material in [15, 24]. Our framework provides a flexible way to consider hidden regular variation and allows simultaneous regular-variation properties to exist at different scales and provides potential for more accurate(More)
Multivariate extreme value theory assumes a multivariate domain of attraction condition for the distribution of a random vector necessitating that each component satisfy a marginal domain of attraction condition. Heffernan and Tawn (2004) and Heffernan and Resnick (2007) developed an approximation to the joint distribution of the random vector by(More)