On Extremal Index of max-stable stationary processes

In this contribution we discuss the relation between Pickands-type constants defined for certain Brown-Resnick stationary process $W(t),t\in R$ as $$\mathcal{H}_W^\delta= \lim_{T\to\infty} T^{-1} E{ \left(\sup_{t\in \delta Z \cap [0,T]} e^{W(t)}\right) },\ \delta \ge 0$$ (set $0 Z=R$ if $\delta=0$) and the extremal index of the associated max-stable stationary process $\xi_W$. We derive several new formulas and obtain lower bounds for $\mathcal{H}_W^\delta$ if $W$ is a Gaussian or a L\'evy process. As a by-product we show an interesting relation between Pickands constants and lower tail probabilities for fractional Brownian motions.Comment: 24 page

African dimensions: essays in honor of William O. Brown

This item was digitized by the Internet Archive.Gulliver, P. H. A land dispute in Arusha, Tanzania. -- Colson, E. Changing anthropology in Africa.--Marcus, H. G. The British and the Ethiopian railway.-- Bennett, N. R. Isike, Ntemi of Unyanyembe. -- Brooks, G. E. Goree and the Cape Verde Rivers. -- Wheeler, D. L. Rebels and rebellions in Angola, 1672-1892. -- Stultz, N. M. The separatist challenge to white domination in South Africa. -- Bustin, E. Government policy toward African cult movements. -- Montgomery, J. D. The Infrastructure of technical assistance. -- Resnick, I. N. Manpower requirements and allocation of educational resources in underdeveloped countries. -- Berg, E. J. A comparative analysis of industrial relations systems in French West Africa and the Gold Coast. -- Karp, M. The "Protestant Ethic" of the Mourids of Senegal

Remembering Frank Cunningham

Friends and colleagues of Frank Cunningham share their tributes in celebration and remembrance of Frank's scholarly and political contributions over a remarkable lifetime. The collection is dedicated to Frank and to his wife, Maryka Omatsu. Includes contributions from: Joseph Carens, Carol Gould, Michael Wade Donnelly, Melissa Williams, Ian Angus, Yoshikazu Nakatani, Esteve Morera, Edward Andrew, Seth Klein, Marjorie Griffin Cohen, Mario Reale, Peter H, Russell, Derek Allen, Kennedy Stewart, Michal Bodemann, Richard Stren, Igor Shoikhedbrod, Nicolas Blomley, Wayne Sumner, Ronald Beiner, Richard Sandbrook, Ingrid Leman Stefanovic, Philip Resnick, and Harry Glasbeek.  Tributes were collected by Elaine Coburn and production by Sean Cain of Better World Communications

Review: Marcia Resnick: As It Is or Could Be

Book review by Marcia Resnick: As It Is or Could Be by Frank H. Goodyear III et al. Yale University Press, March 2022. 208 p. ill. ISBN 978-0-300-25465-5 (h/c), $50.00. Reviewed May 2022 by Claire Payne, Web Services and Data Librarian, Stony Brook University, [email protected]

Maxima of independent, non-identically distributed Gaussian vectors

Let $X_{i,n},n\in \mathbb{N},1\leq i\leq n$, be a triangular array of independent $\mathbb{R}^d$-valued Gaussian random vectors with correlation matrices $\Sigma_{i,n}$. We give necessary conditions under which the row-wise maxima converge to some max-stable distribution which generalizes the class of H\"{u}sler-Reiss distributions. In the bivariate case, the conditions will also be sufficient. Using these results, new models for bivariate extremes are derived explicitly. Moreover, we define a new class of stationary, max-stable processes as max-mixtures of Brown-Resnick processes. As an application, we show that these processes realize a large set of extremal correlation functions, a natural dependence measure for max-stable processes. This set includes all functions $\psi(\sqrt{\gamma(h)}),h\in \mathbb{R}^d$, where $\psi$ is a completely monotone function and $\gamma$ is an arbitrary variogram.Comment: Published at http://dx.doi.org/10.3150/13-BEJ560 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

A Discussion on Mean Excess Plots

A widely used tool in the study of risk, insurance and extreme values is the mean excess plot. One use is for validating a generalized Pareto model for the excess distribution. This paper investigates some theoretical and practical aspects of the use of the mean excess plot.Comment: 26 pages, 9 figure