On Upper and Lower Extremes in Stationary Sequences
Author | : Richard A. Davis |
Publisher | : |
Total Pages | : 42 |
Release | : 1983 |
Genre | : Random variables |
ISBN | : |
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Author | : Richard A. Davis |
Publisher | : |
Total Pages | : 42 |
Release | : 1983 |
Genre | : Random variables |
ISBN | : |
Author | : M. R. Leadbetter |
Publisher | : Springer Science & Business Media |
Total Pages | : 344 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461254493 |
Classical Extreme Value Theory-the asymptotic distributional theory for maxima of independent, identically distributed random variables-may be regarded as roughly half a century old, even though its roots reach further back into mathematical antiquity. During this period of time it has found significant application-exemplified best perhaps by the book Statistics of Extremes by E. J. Gumbel-as well as a rather complete theoretical development. More recently, beginning with the work of G. S. Watson, S. M. Berman, R. M. Loynes, and H. Cramer, there has been a developing interest in the extension of the theory to include, first, dependent sequences and then continuous parameter stationary processes. The early activity proceeded in two directions-the extension of general theory to certain dependent sequences (e.g., Watson and Loynes), and the beginning of a detailed theory for stationary sequences (Berman) and continuous parameter processes (Cramer) in the normal case. In recent years both lines of development have been actively pursued.
Author | : M. R. Leadbetter |
Publisher | : |
Total Pages | : 190 |
Release | : 1979 |
Genre | : |
ISBN | : |
Author | : M. R. Leadbetter |
Publisher | : |
Total Pages | : 103 |
Release | : 1979 |
Genre | : |
ISBN | : |
This report considers the generalization of classical extreme value theory for independent random variables, to apply to stationary stochastic processes. Part 1 is concerned with stochastic sequences and part 2 will deal with continuous time processs. (Author).
Author | : M. R. Leadbetter |
Publisher | : |
Total Pages | : 27 |
Release | : 1982 |
Genre | : |
ISBN | : |
Extensions of classical extreme value theory to apply to stationary sequences generally make use of two types of dependence restriction: (a) a weak 'mixing condition' restricting long range dependence; and (b) a local condition restricting the 'clustering' of high level exceedances. The purpose of this paper is to investigate extremal properties when the local condition (b) is omitted. It is found that, under general conditions, the type of the limiting distribution for maxima is unaltered. The precise modifications and degree of clustering of high level exceedances are found to be largely described by a parameter here called the 'extremal index' of the sequence. (Author).
Author | : M. R. Leadbetter |
Publisher | : |
Total Pages | : 23 |
Release | : 1978 |
Genre | : |
ISBN | : |
Certain aspects of extremal theory for stationary sequences and continuous parameter stationary processes, are discussed in this paper. A slightly modified form of a previously used dependence condition, leads to simple proofs of some key results in extremal theory of stationary sequences. Dependence conditions of a 'weak mixing' type are introduced for continuous parameter stationary processes and results of classical extreme value theory extended to that context. (Author).
Author | : Holger Rootzén |
Publisher | : |
Total Pages | : 34 |
Release | : 1981 |
Genre | : |
ISBN | : |
Author | : Tailen Hsing |
Publisher | : |
Total Pages | : 52 |
Release | : 1988 |
Genre | : Convergence |
ISBN | : |
A distributional mixing condition is introduced for stationary sequences of random vectors to study their extremes. For a sequence satisfying the condition, the following topics which concern the weak limit F of properly normalized partial maxima are studied: (1) To obtain characterizations of F. (2) To study a condition under which the partial maxima behave as they would if the sequence were i.i.d. (3) To consider problems in connection with the independence of the margins of F.
Author | : Valerio Lucarini |
Publisher | : John Wiley & Sons |
Total Pages | : 325 |
Release | : 2016-04-25 |
Genre | : Mathematics |
ISBN | : 1118632192 |
Written by a team of international experts, Extremes and Recurrence in Dynamical Systems presents a unique point of view on the mathematical theory of extremes and on its applications in the natural and social sciences. Featuring an interdisciplinary approach to new concepts in pure and applied mathematical research, the book skillfully combines the areas of statistical mechanics, probability theory, measure theory, dynamical systems, statistical inference, geophysics, and software application. Emphasizing the statistical mechanical point of view, the book introduces robust theoretical embedding for the application of extreme value theory in dynamical systems. Extremes and Recurrence in Dynamical Systems also features: • A careful examination of how a dynamical system can serve as a generator of stochastic processes • Discussions on the applications of statistical inference in the theoretical and heuristic use of extremes • Several examples of analysis of extremes in a physical and geophysical context • A final summary of the main results presented along with a guide to future research projects • An appendix with software in Matlab® programming language to help readers to develop further understanding of the presented concepts Extremes and Recurrence in Dynamical Systems is ideal for academics and practitioners in pure and applied mathematics, probability theory, statistics, chaos, theoretical and applied dynamical systems, statistical mechanics, geophysical fluid dynamics, geosciences and complexity science. VALERIO LUCARINI, PhD, is Professor of Theoretical Meteorology at the University of Hamburg, Germany and Professor of Statistical Mechanics at the University of Reading, UK. DAVIDE FARANDA, PhD, is Researcher at the Laboratoire des science du climat et de l’environnement, IPSL, CEA Saclay, Université Paris-Saclay, Gif-sur-Yvette, France. ANA CRISTINA GOMES MONTEIRO MOREIRA DE FREITAS, PhD, is Assistant Professor in the Faculty of Economics at the University of Porto, Portugal. JORGE MIGUEL MILHAZES DE FREITAS, PhD, is Assistant Professor in the Department of Mathematics of the Faculty of Sciences at the University of Porto, Portugal. MARK HOLLAND, PhD, is Senior Lecturer in Applied Mathematics in the College of Engineering, Mathematics and Physical Sciences at the University of Exeter, UK. TOBIAS KUNA, PhD, is Associate Professor in the Department of Mathematics and Statistics at the University of Reading, UK. MATTHEW NICOL, PhD, is Professor of Mathematics at the University of Houston, USA. MIKE TODD, PhD, is Lecturer in the School of Mathematics and Statistics at the University of St. Andrews, Scotland. SANDRO VAIENTI, PhD, is Professor of Mathematics at the University of Toulon and Researcher at the Centre de Physique Théorique, France.
Author | : J. Tiago de Oliveira |
Publisher | : Springer Science & Business Media |
Total Pages | : 690 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 9401730695 |
The first references to statistical extremes may perhaps be found in the Genesis (The Bible, vol. I): the largest age of Methu'selah and the concrete applications faced by Noah-- the long rain, the large flood, the structural safety of the ark --. But as the pre-history of the area can be considered to last to the first quarter of our century, we can say that Statistical Extremes emer ged in the last half-century. It began with the paper by Dodd in 1923, followed quickly by the papers of Fre-chet in 1927 and Fisher and Tippett in 1928, after by the papers by de Finetti in 1932, by Gumbel in 1935 and by von Mises in 1936, to cite the more relevant; the first complete frame in what regards probabilistic problems is due to Gnedenko in 1943. And by that time Extremes begin to explode not only in what regards applications (floods, breaking strength of materials, gusts of wind, etc. ) but also in areas going from Proba bility to Stochastic Processes, from Multivariate Structures to Statistical Decision. The history, after the first essential steps, can't be written in few pages: the narrow and shallow stream gained momentum and is now a huge river, enlarging at every moment and flooding the margins. Statistical Extremes is, thus, a clear-cut field of Probability and Statistics and a new exploding area for research.