This review paper focuses on statistical issues arising in modeling univariate extremes of a
random sample. In the last three decades there has been a shift from the area of parametric …

The gradient noise (GN) in the stochastic gradient descent (SGD) algorithm is often
considered to be Gaussian in the large data regime by assuming that the classical central …

Long-memory, or more generally fractal, processes are known to play an important role in
many scientific disciplines and applied fields such as physics, geophysics, hydrology …

This volume provides an up-to-date coverage of the theory and applications of ordered
random variables and their functions. Furthermore, it develops the distribution theory of OS …

Research in the statistical analysis of extreme values has flourished over the past decade:
new probability models, inference and data analysis techniques have been introduced; and …

This comprehensive text gives an interesting and useful blend of the mathematical,
probabilistic and statistical tools used in heavy-tail analysis. Heavy tails are characteristic of …

Heavy-tailed distributions are often encountered in economics, finance, biology,
telecommunications, geology, etc. The heaviness of a tail is measured by a tail index …

Huge data sets from the teletraffic industry exhibit many nonstandard characteristics such as
heavy tails and long range dependence. Various estimation methods for heavy tailed time …

In this paper we are interested in an adequate estimation of the dominant component of the
bias of Hill's estimator of a positive tail index γ, in order to remove it from the classical Hill …

The study of the tail behaviour of extreme event distributions is important in several fields
such as hydrology, finance, and telecommunications. Based on two classifications and five …