In this article we study the maximum queue length M in a busy cycle in the M/G/1 queue. Assume that the service times have a logconvex density. For such (heavy tailed) service time distributions the Foreground Background service discipline is optimal. This discipline gives service to those customer(s) that have received the least amount of service so far. It will be shown that under this discip...

We propose a model for the World Wide Web graph that couples the topological growth with the traffic’s dynamical evolution. The model is based on a simple traffic-driven dynamics and generates weighted directed graphs exhibiting the statistical properties observed in the Web. In particular, the model yields a non-trivial time evolution of vertices and heavy-tail distributions for the topologica...

In this paper, the flexible semi-parametric model introduced in is considered for conducting tail inference of censored data. Both and censoring variables are supposed to belong family distributions, thus solutions modelling data which between Weibull-tail Pareto-tail behaviours proposed. Estimators parameters extreme quantiles defined without prior knowledge strength asymptotic normality resul...

Distributions derived from the maximization of Rényi-Tsallis entropy are often called Tsallis’ distributions. We first indicate that these distributions can arise as mixtures, and can be interpreted as the solution of a standard maximum entropy problem with fluctuating constraints. Considering that Tsallis’ distributions appear for systems with displaced or fluctuating equilibriums, we show tha...

Heavy tailed distributions have a big role in studying risk data sets. Statisticians many cases search and try to find new or relatively statistical models fit sets different fields. This article introduced heavy-tailed model by using alpha power transformation exponentiated log-logistic distribution which called distribution. Its properties were derived mathematically such as moments, moment g...

New notions of tail and nontail dependence are used to characterize separately extremal and nonextremal information, including tail log-exceedances and events, and tail-trimmed levels. We prove that near epoch dependence (McLeish, 1975; Gallant and White, 1988) and L0-approximability (Pötscher and Prucha, 1991) are equivalent for tail events and tail-trimmed levels, ensuring a Gaussian central ...

An adaptive direct numerical integration (DNI) algorithm is developed for inverting characteristic functions of compound distributions, enabling efficient computations of high quantiles and conditional Value at Risk (CVaR). A key innovation of the numerical scheme is an effective tail integration approximation that reduces the truncation errors significantly. High precision results of the 0.999...

We consider the analysis of time series data, with particular emphasis on series which have a heavy-tailed structure | that is, whose marginal distributions have a right tail which is regularly varying at innnity with index ?. A natural model to attempt to t to time series data is an autoregression of order p, where p itself is often determined from the data. Recently several methods of paramet...

Due to synoptic-climatological reasons as well as a specific configuration of mountain ranges, the northeast part of the Czech Republic is an area with an enhanced influence of low-pressure systems of the Mediterranean origin. They are associated with an upper-level advection of warm and moist air and often lead to heavy precipitation events. Particularities of this area are evaluated using a r...

Abstract. The temporal communication patterns of human individuals are known to be inhomogeneous or bursty, which is reflected as the heavy tail behavior in the interevent time distribution. As the cause of such bursty behavior two main mechanisms have been suggested: a) Inhomogeneities due to the circadian and weekly activity patterns and b) inhomogeneities rooted in human task execution behav...