Related papers: Generalised extreme value statistics and sum of co…
The general limit distributions of the sum of random variables described by a finite matrix product ansatz are characterized. Using a mapping to a Hidden Markov Chain formalism, non-standard limit distributions are obtained, and related to…
Consider $n$ i.i.d. random elements on $C[0,1]$. We show that, under an appropriate strengthening of the domain of attraction condition, natural estimators of the extreme-value index, which is now a continuous function, and the normalizing…
Estimation of extreme conditional quantiles is often required for risk assessment of natural hazards in climate and geo-environmental sciences and for quantitative risk management in statistical finance, econometrics, and actuarial…
The standard central limit theorem with a Gaussian attractor for the sum of independent random variables may lose its validity in presence of strong correlations between the added random contributions. Here, we study this problem for…
The renormalization group transformation for extreme value statistics of independent, identically distributed variables, recently introduced to describe finite size effects, is presented here in terms of a partial differential equation…
In this paper, we study the asymptotic behavior of the extreme eigenvalues and eigenvectors of the high dimensional spiked sample covariance matrices, in the supercritical case when a reliable detection of spikes is possible. Especially, we…
In this paper, we view fluctuating fronts made of particles on a one-dimensional lattice as an extreme value problem. The idea is to denote the configuration for a single front realization at time $t$ by the set of co-ordinates…
The probability that the sum of independent, centered, identically distributed, heavy-tailed random variables achieves a very large value is asymptotically equal to the probability that there exists a single summand equalling that value. We…
We present evidence that the best model for empirical volume-price distributions is not always the same and it strongly depends in (i) the region of the volume-price spectrum that one wants to model and (ii) the period in time that is being…
The (general) hypoexponential distribution is the distribution of a sum of independent exponential random variables. We consider the particular case when the involved exponential variables have distinct rate parameters. We prove that the…
We investigate correlation time numerically in extremal self-organized critical models, namely, the Bak-Sneppen evolution and the Robin Hood dynamics. The (fitness) correlation time is the duration required for the extinction or mutation of…
The "typical" asymptotic behavior of the weighted sums of independent, identically distibuted random vectors in k-dimensional space is considered. It is shown that under finitnes of fifth absolute moment of an individual term the rate of…
We briefly review Boltzmann-Gibbs and nonextensive statistical mechanics as well as their connections with Fokker-Planck equations and with existing central limit theorems. We then provide some hints that might pave the road to the proof of…
We consider a general class of round-robin tournament models of equally strong players. In these models, each of the $n$ players competes against every other player exactly once. For each match between two players, the outcome is a value…
Our contribution is to widen the scope of extreme value analysis applied to discrete-valued data. Extreme values of a random variable $X$ are commonly modeled using the generalized Pareto distribution, a method that often gives good results…
The maximum correlation of functions of a pair of random variables is an important measure of stochastic dependence. It is known that this maximum nonlinear correlation is identical to the absolute value of the Pearson correlation for a…
Extremization of the Boltzmann-Gibbs (BG) entropy under appropriate norm and width constraints yields the Gaussian distribution. Also, the basic solutions of the standard Fokker-Planck (FP) equation (related to the Langevin equation with…
We consider the distribution of the major index on standard tableaux of arbitrary straight shape and certain skew shapes. We use cumulants to classify all possible limit laws for any sequence of such shapes in terms of a simple auxiliary…
Testing whether two multivariate samples exhibit the same extremal behavior is an important problem in various fields including environmental and climate sciences. While several ad-hoc approaches exist in the literature, they often lack…
We consider the distribution of the sum and the maximum of a collection of independent exponentially distributed random variables. The focus is laid on the explicit form of the density functions (pdf) of non-i.i.d. sequences. Those are…