000			03839nam a22004815i 4500
001			978-3-0348-0009-9
003			DE-He213
005			20140220083738.0
007			cr nn 008mamaa
008			101013s2011 sz | s |||| 0|eng d
020			_a9783034800099 _9978-3-0348-0009-9
024	7		_a10.1007/978-3-0348-0009-9 _2doi
050		4	_aQA273.A1-274.9
050		4	_aQA274-274.9
072		7	_aPBT _2bicssc
072		7	_aPBWL _2bicssc
072		7	_aMAT029000 _2bisacsh
082	0	4	_a519.2 _223
100	1		_aFalk, Michael. _eauthor.
245	1	0	_aLaws of Small Numbers: Extremes and Rare Events _h[electronic resource] / _cby Michael Falk, Jürg Hüsler, Rolf-Dieter Reiss.
264		1	_aBasel : _bSpringer Basel, _c2011.
300			_aXVI, 509p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aPreface to the Third Edition -- Preface to the Second Edition -- Preface to the First Edition -- Part I. The IID Case: Functional Laws Of Small Numbers -- 1 Functional Laws of Small Numbers -- 2 Extreme Value Theory -- 3 Estimation of Conditional Curves -- Part II. The IID Case: Multivariate Extremes -- 4 Basic Theory of Multivariate Maxima -- 5 Multivariate Generalized Pareto Distributions -- 6 The Pickands Approach in the Bivariate Case -- 7 Multivariate Extremes: Supplementary Concepts and Results -- Part III. Non-IID Observations -- 8 Introduction to the Non-IID Case -- 9 Extremes of Random Sequences -- 10 Extremes of Gaussian Processes -- 11 Extensions for Rare Events -- 12 Statistics of Extremes -- Author Index -- Subject Index -- Bibliography.
520			_aSince 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
650		0	_aMathematics.
650		0	_aDistribution (Probability theory).
650		0	_aMathematical statistics.
650	1	4	_aMathematics.
650	2	4	_aProbability Theory and Stochastic Processes.
650	2	4	_aStatistical Theory and Methods.
700	1		_aHüsler, Jürg. _eauthor.
700	1		_aReiss, Rolf-Dieter. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783034800082
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-0348-0009-9
912			_aZDB-2-SMA
999			_c106577 _d106577