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We study non-stationary stochastic processes arising from sequential dynamical systems built on maps with a neutral fixed points and prove the existence of Extreme Value Laws for such processes. We use an approach developed in \cite{FFV16},…

Dynamical Systems · Mathematics 2017-07-17 Ana Cristina Moreira Freitas , Jorge Milhazes Freitas , Sandro Vaienti

The extreme value statistics of active matter offer significant insight into their unique properties. A phase transition has recently been reported in a model of branching run-and-tumble particles, describing the spatial spreading of an…

Statistical Mechanics · Physics 2020-06-11 Bertrand Lacroix-A-Chez-Toine , Asaf Miron

We study the linear eigenvalue statistics of large random graphs in the regimes when the mean number of edges for each vertex tends to infinity. We prove that for a rather wide class of test functions the fluctuations of linear eigenvalue…

Mathematical Physics · Physics 2015-06-03 Maria Shcherbina , Brunello Tirozzi

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…

Computation · Statistics 2009-02-03 Tewfik Kernane , Zohrh A. Raizah

We present a generalization of the maximal inequalities that upper bound the expectation of the maximum of $n$ jointly distributed random variables. We control the expectation of a randomly selected random variable from $n$ jointly…

Probability · Mathematics 2017-08-31 Jiantao Jiao , Yanjun Han , Tsachy Weissman

For a skew normal random sequence, convergence rates of the distribution of its partial maximum to the Gumbel extreme value distribution are derived. The asymptotic expansion of the distribution of the normalized maximum is given under an…

Methodology · Statistics 2012-12-06 Xin Liao , Zuoxiang Peng , Saralees Nadarajah , Xiaoqian Wang

The aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution. Conditions for this convergence to…

Probability · Mathematics 2011-10-20 Katarzyna Bartkiewicz , Adam Jakubowski , Thomas Mikosch , Olivier Wintenberger

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…

Methodology · Statistics 2022-07-26 Yongxin Li , Liujun Chen , Deyuan Li , Hansheng Wang

Encouraged by the study of extremal limits for sums of the form $$\lim_{N\to\infty}\frac{1 }{N}\sum_{n=1}^N c(x_n,y_n)$$ with uniformly distributed sequences $\{x_n\},\,\{y_n\}$ the following extremal problem is of interest…

Optimization and Control · Mathematics 2015-02-25 Maria Rita Iacò , Stefan Thonhauser , Robert F. Tichy

In this paper, we obtain general representations for the joint distributions and copulas of arbitrary dependent random variables absolutely continuous with respect to the product of given one-dimensional marginal distributions. The…

Statistics Theory · Mathematics 2016-08-16 Victor H. de la Peña , Rustam Ibragimov , Shaturgun Sharakhmetov

A network evolution with predicted tail and extremal indices of PageRank and the Max-Linear Model used as node influence indices in random graphs is considered. The tail index shows a heaviness of the distribution tail. The extremal index…

Statistics Theory · Mathematics 2022-11-28 Natalia Markovich

We consider stationary configurations of points in Euclidean space which are marked by positive random variables called scores. The scores are allowed to depend on the relative positions of other points and outside sources of randomness.…

Probability · Mathematics 2025-06-25 Bojan Basrak , Ilya Molchanov , Hrvoje Planinić

In this work, we revisit the estimation of the model parameters of a Weibull distribution based on iid observations, using the maximum likelihood estimation (MLE) method which does not yield closed expressions of the estimators. Among other…

Computation · Statistics 2025-01-22 Buu-Chau Truong , Peter Mphekgwana , Nabendu Pal

We derive exact expressions for the finite-time statistics of extrema (maximum and minimum) of the spatial displacement and the fluctuating entropy flow of biased random walks. Our approach captures key features of extreme events in…

Statistical Mechanics · Physics 2021-02-10 Alexandre Guillet , Édgar Roldán , Frank Jülicher

Extreme events are an important theme in various areas of science because of their typically devastating effects on society and their scientific complexities. The latter is particularly true if the underlying dynamics does not lead to…

Data Analysis, Statistics and Probability · Physics 2015-05-30 Aicko Yves Schumann , Nicholas R. Moloney , Jörn Davidsen

This paper addresses the problem of estimating the extreme value index in presence of random censoring for distributions in the Weibull domain of attraction. The methodologies introduced in [Worms (2014)], in the heavy-tailed case, are…

Statistics Theory · Mathematics 2015-06-12 Julien Worms , Rym Worms

We study the statistical distribution of the closest encounter between generic smooth observations computed along different trajectories of a rapidly mixing dynamical system. At the limit of large trajectories, we obtain a distribution of…

Chaotic Dynamics · Physics 2022-08-31 Theophile Caby

We propose some new results on the comparison of the minimum or maximum order statistic from a random number of non-identical random variables. Under the non-identical set-up, with certain conditions, we prove that random minimum (maximum)…

Statistics Theory · Mathematics 2024-03-08 Amarjit Kundu , Shovan Chowdhury , Bidhan Modok

It is well-known that the expected scaled maximum of non-negative random variables with unit mean defines a stable tail dependence function associated with some extreme-value copula. In the special case when these random variables are…

Methodology · Statistics 2018-05-30 Jan-Frederik Mai

Extremal quantile regression, i.e. quantile regression applied to the tails of the conditional distribution, counts with an increasing number of economic and financial applications such as value-at-risk, production frontiers, determinants…

Methodology · Statistics 2022-01-24 Victor Chernozhukov , Iván Fernández-Val , Tetsuya Kaji