|
" Laws of small numbers : "
Michael Falk, Jürg Hüsler, Rolf-Dieter Reiss.
| Document Type
|
:
|
BL
|
| Record Number
|
:
|
1013979
|
| Doc. No
|
:
|
b768349
|
| Main Entry
|
:
|
Falk, Michael,1954-
|
| Title & Author
|
:
|
Laws of small numbers : : extremes and rare events /\ Michael Falk, Jürg Hüsler, Rolf-Dieter Reiss.
|
| Edition Statement
|
:
|
3rd, rev. and extended ed.
|
| Publication Statement
|
:
|
Basel :: Birkhäuser :: Springer,, ©2011.
|
| Page. NO
|
:
|
1 online resource (xv, 509 pages)
|
| ISBN
|
:
|
3034800096
|
|
|
:
|
: 9783034800099
|
|
|
:
|
3034800088
|
|
|
:
|
9783034800082
|
| Bibliographies/Indexes
|
:
|
Includes bibliographical references and indexes.
|
| Contents
|
:
|
The IID case, functional laws of small numbers -- Functional laws of small numbers -- Extreme value theory -- Estimation of conditional curves -- The IID case, multivariate extremes -- Basic theory of multivariate extremes -- Multivariate generalized pareto distributions -- The pickands approach in the Bivariate case -- Multivariate extremes, supplementary concepts and results -- Non-IID observations -- Introduction to the non-IID case -- Extremes of random sequences -- Extremes of Gaussian processes -- Extensions for rare events -- Statistics of extremes.
|
| Abstract
|
:
|
Since the publication of the first edition of this seminar book in 1994, the theory and applications of extremes and rare events have enjoyed an enormous and still increasing interest. The intention of the book is to give a mathematically oriented development of the theory of rare events underlying various applications. This characteristic of the book was strengthened in the second edition by incorporating various new results. In this third edition, the dramatic change of focus of extreme value theory has been taken into account: from concentrating on maxima of observations it has shifted to large observations, defined as exceedances over high thresholds. One emphasis of the present third edition lies on multivariate generalized Pareto distributions, their representations, properties such as their peaks-over-threshold stability, simulation, testing and estimation. Reviews of the 2nd edition: "In brief, it is clear that this will surely be a valuable resource for anyone involved in, or seeking to master, the more mathematical features of this field." David Stirzaker, Bulletin of the London Mathematical Society "Laws of Small Numbers can be highly recommended to everyone who is looking for a smooth introduction to Poisson approximations in EVT and other fields of probability theory and statistics. In particular, it offers an interesting view on multivariate EVT and on EVT for non-iid observations, which is not presented in a similar way in any other textbook." Holger Drees, Metrika.
|
| Subject
|
:
|
Extreme value theory.
|
| Subject
|
:
|
Multivariate analysis.
|
| Subject
|
:
|
Extreme value theory.
|
| Subject
|
:
|
MATHEMATICS-- Probability Statistics-- General.
|
| Subject
|
:
|
Multivariate analysis.
|
| Dewey Classification
|
:
|
515/.782
|
| LC Classification
|
:
|
QA273.6.F35 2011
|
| Added Entry
|
:
|
Hüsler, J., (Jürg)
|
|
|
:
|
Reiss, R.-D., (Rolf-Dieter)
|
| |