05343nam 22006374a 450 991014472330332120170810191454.01-280-54155-597866105415530-470-01238-20-470-01237-4(CKB)1000000000377256(EBL)427979(OCoLC)437111555(SSID)ssj0000310331(PQKBManifestationID)11229909(PQKBTitleCode)TC0000310331(PQKBWorkID)10289289(PQKB)10483159(MiAaPQ)EBC427979(PPN)190734582(EXLCZ)99100000000037725620040616d2004 uy 0engur|n|---|||||txtccrStatistics of extremes[electronic resource] theory and applications /Jan Beirlant ... [et al.], with contributions from Daniel De Waal, Chris FerroHoboken, NJ Wiley20041 online resource (514 p.)Wiley series in probability and statisticsDescription based upon print version of record.0-471-97647-4 Includes bibliographical references (p. 461-478) and indexes.Statistics of Extremes; Contents; Preface; 1 WHY EXTREME VALUE THEORY?; 1.1 A Simple Extreme Value Problem; 1.2 Graphical Tools for Data Analysis; 1.2.1 Quantile-quantile plots; 1.2.2 Excess plots; 1.3 Domains of Applications; 1.3.1 Hydrology; 1.3.2 Environmental research and meteorology; 1.3.3 Insurance applications; 1.3.4 Finance applications; 1.3.5 Geology and seismic analysis; 1.3.6 Metallurgy; 1.3.7 Miscellaneous applications; 1.4 Conclusion; 2 THE PROBABILISTIC SIDE OF EXTREME VALUE THEORY; 2.1 The Possible Limits; 2.2 An Example; 2.3 The Fréchet-Pareto Case: g > 02.3.1 The domain of attraction condition2.3.2 Condition on the underlying distribution; 2.3.3 The historical approach; 2.3.4 Examples; 2.3.5 Fitting data from a Pareto-type distribution; 2.4 The (Extremal) Weibull Case: g < 0; 2.4.1 The domain of attraction condition; 2.4.2 Condition on the underlying distribution; 2.4.3 The historical approach; 2.4.4 Examples; 2.5 The Gumbel Case: g = 0; 2.5.1 The domain of attraction condition; 2.5.2 Condition on the underlying distribution; 2.5.3 The historical approach and examples; 2.6 Alternative Conditions for (C(g))2.7 Further on the Historical Approach2.8 Summary; 2.9 Background Information; 2.9.1 Inverse of a distribution; 2.9.2 Functions of regular variation; 2.9.3 Relation between F and U; 2.9.4 Proofs for section 2.6; 3 AWAY FROM THE MAXIMUM; 3.1 Introduction; 3.2 Order Statistics Close to the Maximum; 3.3 Second-order Theory; 3.3.1 Remainder in terms of U; 3.3.2 Examples; 3.3.3 Remainder in terms of F; 3.4 Mathematical Derivations; 3.4.1 Proof of (3.6); 3.4.2 Proof of (3.8); 3.4.3 Solution of (3.15); 3.4.4 Solution of (3.18); 4 TAIL ESTIMATION UNDER PARETO-TYPE MODELS; 4.1 A Naive Approach4.2 The Hill Estimator4.2.1 Construction; 4.2.2 Properties; 4.3 Other Regression Estimators; 4.4 A Representation for Log-spacings and Asymptotic Results; 4.5 Reducing the Bias; 4.5.1 The quantile view; 4.5.2 The probability view; 4.6 Extreme Quantiles and Small Exceedance Probabilities; 4.6.1 First-order estimation of quantiles and return periods; 4.6.2 Second-order refinements; 4.7 Adaptive Selection of the Tail Sample Fraction; 5 TAIL ESTIMATION FOR ALL DOMAINS OF ATTRACTION; 5.1 The Method of Block Maxima; 5.1.1 The basic model; 5.1.2 Parameter estimation5.1.3 Estimation of extreme quantiles5.1.4 Inference: confidence intervals; 5.2 Quantile View-Methods Based on (C(g)); 5.2.1 Pickands estimator; 5.2.2 The moment estimator; 5.2.3 Estimators based on the generalized quantile plot; 5.3 Tail Probability View-Peaks-Over-Threshold Method; 5.3.1 The basic model; 5.3.2 Parameter estimation; 5.4 Estimators Based on an Exponential Regression Model; 5.5 Extreme Tail Probability, Large Quantile and Endpoint Estimation Using Threshold Methods; 5.5.1 The quantile view; 5.5.2 The probability view; 5.5.3 Inference: confidence intervals5.6 Asymptotic Results Under (C(g))-(C*(g))Research in the statistical analysis of extreme values has flourished over the past decade: new probability models, inference and data analysis techniques have been introduced; and new application areas have been explored. Statistics of Extremes comprehensively covers a wide range of models and application areas, including risk and insurance: a major area of interest and relevance to extreme value theory. Case studies are introduced providing a good balance of theory and application of each model discussed, incorporating many illustrated examples and plots of data. The last part of the Wiley series in probability and statistics.Mathematical statisticsMaxima and minimaMathematical statistics.Maxima and minima.519.5Beirlant Jan320748MiAaPQMiAaPQMiAaPQBOOK9910144723303321Statistics of extremes754749UNINA