Traffic measurements from communication networks have shown that many quantities charecterizing network performance have long-tail probability distributions, i.e., with tails that decay more slowly than exponentially. File lengths, call holding times, scene lengths in MPEG video streams, and intervals between connection requests in Internet traffic all have been found to have long-tail distribu...

Applying the results about harmonic moments of classical Galton-Watson process, we obtain deviations for random sums indexed by generations a branching process. Our show that decay rates large and moderate depend heavily on degree heavy tail asymptotic distributions normalizing constants. If underlying process belongs to Schr?der case, both deviation probabilities three rates, where critical ca...

We provide a complete large and moderate deviations asymptotic for the steady-state waiting time of a class of subexponential M/G/1 queues under heavy traffic. The asymptotic is uniform over the whole positive axis, and reduces to Kingman’s asymptotic and heavy-tail asymptotic on two ends, both of which are known to be valid only in limited regimes. On the link between these two well-known asym...

Estimation of the occurrence of extreme events actually is that of risk premiums interest in actuarial Sciences, Insurance and Finance. Heavy-tailed distributions are used to model large claims and losses. In this paper we deal with the empirical estimation of the distortion risk premiums for heavy tailed losses by using the extreme value statistics. This approach can produce a potential bias i...

An abundance of high quality data sets requiring heavy tailed models necessitates reliable methods of estimating the shape parameter governing the degree of tail heaviness. The Hill estimator is a popular method for doing this but its practical use is encumbered by several diiculties. We show that an alternative method of plotting Hill estimator values is more revealing than the standard method...

Optical rogue waves are demonstrated in the far-field scattered radiation from photonic arrays designed according to aperiodic distributions of prime elements complex quadratic fields. Specifically, by studying light diffraction Eisenstein and Gaussian we establish a connection between formation optical multifractality visible single-scattering regime. We link strong with heavy-tail probability...

Recently, Hahn (2008) has proposed the mixture between the uniform and the beta distributions as an alternative to the beta distribution in PERT methodology which allows for varying amounts of dispersion and a greater likelihood of more extreme tail-area events. However, this mixture lacks a closed cumulative distribution function expression and its parameters remain a difficult interpretation....

This article focuses on simulation-based inference for the time-deformation models directed by a duration process. In order to better capture the heavy tail property of the time series of financial asset returns, the innovation of the observation equation is subsequently assumed to have a Student-t distribution. Suitable Markov chain Monte Carlo (MCMC) algorithms, which are hybrids of Gibbs and...

Efficient estimation of tail probabilities involving heavy tailed random variables is amongst the most challenging problems in Monte-Carlo simulation. In the last few years, applied probabilists have achieved considerable success in developing efficient algorithms for some such simple but fundamental tail probabilities. Usually, unbiased importance sampling estimators of such tail probabilities...