Related papers: Generalised extreme value statistics and sum of co…

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…

Using the proposed by us thinning approach to describe extreme matrices, we find an explicit exponentiation formula linking classical extreme laws of Fr\'echet, Gumbel and Weibull given by Fisher-Tippet-Gnedenko classification and free…

Let $\mathbf{X}(n) \in \mathbb{R}^d$ be a sequence of random vectors, where $n\in\mathbb{N}$ and $d = d(n)$. Under certain weakly dependence conditions, we prove that the distribution of the maximal component of $\mathbf{X}$ and the…

We use extreme value theory to estimate the probability of successive exceedances of a threshold value of a time-series of an observable on several classes of chaotic dynamical systems. The observables have either a Fr\'echet (fat-tailed)…

Let $ k >0 $ be an integer and $ Y $ a standard Gamma$(k)$ distributed random variable. Let $ X $ be an independent positive random variable with a density that is hyperbolically monotone (HM) of order $ k.$ Then $Y\cdot X$ and $Y/X $ both…

We propose a new class of extreme-value copulas which are extreme-value limits of conditional normal models. Conditional normal models are generalizations of conditional independence models, where the dependence among observed variables is…

The asymptotic results that underlie applications of extreme random fields often assume that the variables are located on a regular discrete grid, identified with $\mathbb{Z}^2$, and that they satisfy stationarity and isotropy conditions.…

Let $\{X_i,i=1,2,...\}$ be i.i.d. standard gaussian variables. Let $S_n=X_1+...+X_n$ be the sequence of partial sums and $$ L_n=\max_{0\leq i<j\leq n}\frac{S_j-S_i}{\sqrt{j-i}}. $$ We show that the distribution of $L_n$, appropriately…

We explain the connection between the Gumbel limit for diffusion exit times and the theory of extreme values.

There is an increasing interest to understand the dependence structure of a random vector not only in the center of its distribution but also in the tails. Extreme-value theory tackles the problem of modelling the joint tail of a…

The frequency and magnitude of weather extreme events have increased significantly during the past few years in response to anthropogenic climate change. However, global statistical characteristics and underlying physical mechanisms are…

We investigate the statistics of the maximal fluctuation of two-dimensional Gaussian interfaces. Its relation to the entropic repulsion between rigid walls and a confined interface is used to derive the average maximal fluctuation $<m> \sim…

In many biological, agricultural, military activity problems and in some quality control problems, it is almost impossible to have a fixed sample size, because some observations are always lost for various reasons. Therefore, the sample…

We study largest singular values of large random matrices, each with mean of a fixed rank $K$. Our main result is a limit theorem as the number of rows and columns approach infinity, while their ratio approaches a positive constant. It…

The sum of $N$ sufficiently strongly correlated random variables will not in general be Gaussian distributed in the limit N\to\infty. We revisit examples of sums x that have recently been put forward as instances of variables obeying a…

The generalised extreme value (GEV) distribution is a three parameter family that describes the asymptotic behaviour of properly renormalised maxima of a sequence of independent and identically distributed random variables. If the shape…

We study the statistical distribution of the closest encounter between observations computed along different trajectories of a mixing dynamical system. At the limit of large trajectories, the distribution is of Gumbel type and depends on…

This paper proves several weak limit theorems for the joint version of extreme order statistics and partial sums of independently and identically distributed random variables. The results are also extended to almost sure limit version.

The classical approach to analyzing extreme value data is the generalized Pareto distribution (GPD). When the GPD is used to explain a target variable with the large dimension of covariates, the shape and scale function of covariates…

We derive in this article the exact non-asymptotical exponential and power estimates for self-normalized sums of centered independent random variables (r.v.) under natural norming. We will use also the theory of the so-called Grand Lebesgue…