The tail dependence of multivariate distributions is frequently studied via the tool of copulas. This paper develops a general method, which is based on multivariate regular variation, to evaluate the tail dependence of heavy-tailed scale mixtures of multivariate distributions, whose copulas are not explicitly accessible. Tractable formulas for tail dependence parameters are derived, and a suff...

Distributions with a heavy tail are difficult to estimate. If the design of an optimal scheduling policy is sensitive to the details of heavy tail distributions of the service times, an approximately optimal solution is difficult to obtain. This paper shows that the optimal scheduling of an M/G/1 queue with heavy tailed service times does not present this difficulty and that an approximately op...

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 the step length and the dimensionality of the search space. The probability decreases fast with increasing st...

Heavy tail probability distributions are important in many scientific disciplines, such as hydrology, geology, and physics among others. To this end many heavy tail distributions are commonly used in practice. In order to determine an appropriate family of distributions for a specified application it is useful to classify the probability law via its tail behavior. Through the use of Parzen’s de...

The multivariate regular variation (MRV) is one of the most important tools in modeling multivariate heavy-tailed phenomena. This paper characterizes the MRV distributions through the tail dependence function of the copula associated with them. Along with some existing results, our studies indicate that the existence of the lower tail dependence function of the survival copula is necessary and ...

Various multivariate Pareto distributions are known to exhibit the heavy tail behaviors. This paper examines the tail dependence properties of a general class of multivariate Pareto distributions with the Pareto index and some common scale parameters. The multivariate tail dependence describes the amount of dependence in the upper-orthant tail or lower-orthant tail of a multivariate distributio...

Heavy tail probability distributions are important in many scientific disciplines such as hydrology, geology, and physics and therefore feature heavily in statistical practice. Rather than specifying a family of heavy-tailed distributions for a given application, it is more common to use a nonparametric approach, where the distributions are classified according to the tail behavior. Through the...