Related papers: An elementary approach to extreme values theory

We exploit the asymptotic normality of the extreme value theory (EVT) based estimators of the parameters of a symmetric L\'evy-stable distribution, to construct confidence intervals. The accuracy of these intervals is evaluated through a…

Extreme value theory is concerned with probabilistic and statistical questions related to very high or very low values in sequences of random variables and in stochastic processes. The subject has a rich mathematical theory and also a long…

This note tries to show that a re-examination of a first course in analysis, using the more sophisticated tools and approaches obtained in later stages, can be a real fun for experts, advanced students, etc. We start by going to the…

Modern statistical analyses often encounter datasets with massive sizes and heavy-tailed distributions. For datasets with massive sizes, traditional estimation methods can hardly be used to estimate the extreme value index directly. To…

This note describes a way of obtaining e that differs from the standard one. It could be used as an alternate way of showing how the value of e is obtained. No attempt is made to show the existence of the limit in the definition of e that…

This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…

An intriguing connection between extreme value statistics and traveling fronts has been found recently in a number of diverse problems. In this brief review we outline a few such problems and consider their various applications.

In environmental applications of extreme value statistics, the underlying stochastic process is often modeled either as a max-stable process in continuous time/space or as a process in the domain of attraction of such a max-stable process.…

Being the limits of copulas of componentwise maxima in independent random samples, extreme-value copulas can be considered to provide appropriate models for the dependence structure between rare events. Extreme-value copulas not only arise…

In many application areas of extreme value theory, the variables of interest are not directly observable but instead contain errors. In this article, we quantify the effect of these errors in moment-based extreme value index estimation, and…

Abstract In Extreme Value methodology the choice of threshold plays an important role in efficient modelling of observations exceeding the threshold. The threshold must be chosen high enough to ensure an unbiased extreme value index but…

Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this paper using fixed point iteration. The commonly used numerical approach for addressing this problem is the Newton-Raphson approach which…

Research on summarization has mainly been driven by empirical approaches, crafting systems to perform well on standard datasets with the notion of information Importance remaining latent. We argue that establishing theoretical models of…

In risk management, often the probability must be estimated that a random vector falls into an extreme failure set. In the framework of bivariate extreme value theory, we construct an estimator for such failure probabilities and analyze its…

We formulate one methodology to put a value or price on knowledge using well accepted techniques from finance. We provide justifications for these finance principles based on the limitations of the physical world we live in. We start with…

We extend the scope of the dynamical theory of extreme values to cover phenomena that do not happen instantaneously, but evolve over a finite, albeit unknown at the onset, time interval. We consider complex dynamical systems, composed of…

This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the…

The paper proposes a new variant of a decision tree, called an Extreme Learning Tree. It consists of an extremely random tree with non-linear data transformation, and a linear observer that provides predictions based on the leaf index where…

Modeling cyber risks has been an important but challenging task in the domain of cyber security. It is mainly because of the high dimensionality and heavy tails of risk patterns. Those obstacles have hindered the development of statistical…

We introduce the notion of multiple extremal integrals as an extension of single extremal integrals, which have played important roles in extreme value theory. The multiple extremal integrals are formulated in terms of a product-form random…