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Statistical Analysis of Extreme Values.pdf
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Statistical Analysis of
Extreme Values
with Applications to Insurance, Finance,
Hydrology and Other Fields
Third Edition
Contents
Preface to the Third Edition . . . . . . . . . . . . . . . . . . . . . . v
Preface to the Second Edition . . . . . . . . . . . . . . . . . . . . . vii
Preface to the First Edition . . . . . . . . . . . . . . . . . . . . . . . ix
List of Special Symbols . . . . . . . . . . . . . . . . . . . . . . . . . xviii
I Modeling and Data Analysis 1
1 Parametric Modeling 3
1.1 Applications of Extreme Value Analysis . . . . . . . . . . . . . . . 3
1.2 Observing Exceedances and Maxima . . . . . . . . . . . . . . . . . 7
1.3 Modeling by Extreme Value Distributions . . . . . . . . . . . . . . 14
1.4 Modeling by Generalized Pareto Distributions . . . . . . . . . . . . 23
1.5 Heavy and Fat–Tailed Distributions . . . . . . . . . . . . . . . . . 30
1.6 Quantiles, Transformations and Simulations . . . . . . . . . . . . . 35
2 Diagnostic Tools 39
2.1 Visualization of Data . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.2 Excess and Hazard Functions . . . . . . . . . . . . . . . . . . . . . 49
2.3 Fitting ParametricDistributions to Data . . . . . . . . . . . . . . . 56
2.4 Q–Q and P–P Plots . . . . . . . . . . . . . . . . . . . . . . . . . . 61
2.5 Trends, Seasonality and Autocorrelation . . . . . . . . . . . . . . . 64
2.6 The Tail Dependence Parameter . . . . . . . . . . . . . . . . . . . 74
2.7 Clustering of Exceedances . . . . . . . . . . . . . . . . . . . . . . . 76
II Statistical Inference in Parametric Models 81
3 An Introduction to Parametric Inference 83
3.1 Estimation in Exponential and Gaussian Models . . . . . . . . . . 84
3.2 Confidence Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.3 Test Procedures and p–Values . . . . . . . . . . . . . . . . . . . . . 93
3.4 Inference in Poisson and Mixed Poisson Models . . . . . . . . . . . 96
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