Statistical Analysis of Extreme Values: with Applications to Insurance, Finance, Hydrology and Other Fields

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Springer Science & Business Media, Aug 8, 2007 - Mathematics - 512 pages
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Statistical analysis of extreme data is vital to many disciplines including hydrology, insurance, finance, engineering and environmental sciences. This book provides a self-contained introduction to parametric modeling, exploratory analysis and statistical interference for extreme values. For this Third Edition, the entire text has been thoroughly updated and rearranged to meet contemporary requirements, with new sections and chapters address such topics as dependencies, the conditional analysis and the multivariate modeling of extreme data. New chapters include An Overview of Reduced-Bias Estimation; The Spectral Decomposition Methodology; About Tail Independence; and Extreme Value Statistics of Dependent Random Variables.

 

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Contents

Parametric Modeling
3
12 Observing Exceedances and Maxima
7
13 Modeling by Extreme Value Distributions
14
14 Modeling by Generalized Pareto Distributions
23
15 Heavy and FatTailed Distributions
30
16 Quantiles Transformations and Simulations
35
Diagnostic Tools
39
22 Excess and Hazard Functions
49
114 Multivariate SumStable Distributions
285
Multivariate Maxima
291
122 The GumbelMcFadden Model
301
123 Estimation in Extreme Value Models
305
124 A Spectral Decomposition Methodology
309
Multivariate Peaks Over Threshold
313
132 Estimation of the Canonical Dependence Function
318
133 About Tail Independence
321

23 Fitting Parametric Distributions to Data
56
24 QQ and PP Plots
61
25 Trends Seasonality and Autocorrelation
64
26 The Tail Dependence Parameter
74
27 Clustering of Exceedances
76
Statistical Inference in Parametric Models
81
An Introduction to Parametric Inference
83
31 Estimation in Exponential and Gaussian Models
84
32 Confidence Intervals
90
33 Test Procedures and pValues
93
34 Inference in Poisson and Mixed Poisson Models
96
35 The Bayesian Estimation Principle
102
Extreme Value Models
107
42 Testing within Extreme Value Models
118
43 Extended Extreme Value Models and Related Models
120
Generalized Pareto Models
127
52 Testing Within Generalized Pareto Models
143
53 Testing Extreme Value Conditions with Applications
144
54 Statistics in PoissonGP Models
152
55 The LogPareto Model and Other ParetoExtensions
154
Advanced Statistical Analysis
159
62 Models of Time Series the Extremal Index
164
63 Statistics for Student Distributions
170
64 Statistics for SumStable Distributions
172
65 Ultimate and Penultimate GP Approximation
182
66 An Overview of ReducedBias Estimation
190
Statistics of Dependent Variables
207
71 The Impact of Serial Dependence
208
72 Estimating the Extreme Value Index
209
73 Extreme Quantile Estimation
215
74 A Time Series Approach
219
Conditional Extremal Analysis
227
a Nonparametric Approach
238
83 Maxima Under Covariate Information
240
84 The Bayesian Estimation Principle Revisited
242
Statistical Models for Exceedance Processes
247
92 Mean and Median TYear Return Levels
250
93 ML and Bayesian Estimation in Models of Poisson Processes
252
94 GP Process Approximations
256
95 Inhomogeneous Poisson Processes Exceedances Under Covariate Information
258
Elements of Multivariate Statistical Analysis
263
Basic Multivariate Concepts and Visualization
264
102 Visualizing Multivariate Data
270
103 Decompositions of Multivariate Distributions
275
Elliptical and Related Distributions
279
112 Spherical and Elliptical Distributions
281
113 Multivariate Student Distributions
283
134 The Point Process Approach to the Multivariate POT Method
333
Topics in Hydrology and Environmental Sciences
335
Flood Frequency Analysis
337
142 Analyzing Partial Duration Series
338
143 Regional Flood Frequency Analysis
343
144 The LMoment Estimation Method
345
145 A Bayesian Approach to Regional Estimation
349
Environmental Sciences
352
152 Inclusion of Covariates
356
153 Example of Trend
359
154 Example of Cycle
361
155 Example of Covariate
364
156 Numerical Methods and Software
367
Extreme Returns in Asset Prices
369
161 Stylized Facts and Historical Remarks
372
162 Empirical Evidence in Returns Series
375
163 Parametric Estimation of the Tails of Returns
378
164 The ProfitLoss Variable and Risk Parameters
382
165 Evaluating the ValueatRisk VaR
386
166 The VaR for a Single Derivative Contract
392
167 GARCH and Stochastic Volatility Structures
395
168 Predicting the Serial Conditional VaR
401
The Impact of Large Claims on Actuarial Decisions
411
171 Numbers of Claims and the Total Claim Amount
412
172 Estimation of the Net Premium
415
173 Segmentation According to the Probable Maximum Loss
419
174 The Risk Process and the TYear Initial Reserve
426
175 Elements of Ruin Theory
432
176 Credibility Bayesian Estimation of the Net Premium
434
Topics in Material and Life Sciences
438
Material Sciences
439
182 Stereology of Extremes
445
Life Science
453
A Regression Approach
458
First Steps towards Xtremes and StatPascal
464
The Menu System
467
A3 Becoming Acquainted with the Menu System
470
A4 Technical Aspects of Xtremes
476
A5 The UserFormula UFO Facilities
481
The StatPascal Programming Language
485
First Steps
486
B2 Plotting Curves
490
B3 Generating and Accessing Data
492
Author Index
495
Subject Index
501
Bibliography
509
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Barrister, Gray's Inn Tax Chambers.

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