## An Introduction to Statistical Modeling of Extreme ValuesDirectly oriented towards real practical application, this book develops both the basic theoretical framework of extreme value models and the statistical inferential techniques for using these models in practice. Intended for statisticians and non-statisticians alike, the theoretical treatment is elementary, with heuristics often replacing detailed mathematical proof. Most aspects of extreme modeling techniques are covered, including historical techniques (still widely used) and contemporary techniques based on point process models. A wide range of worked examples, using genuine datasets, illustrate the various modeling procedures and a concluding chapter provides a brief introduction to a number of more advanced topics, including Bayesian inference and spatial extremes. All the computations are carried out using S-PLUS, and the corresponding datasets and functions are available via the Internet for readers to recreate examples for themselves. An essential reference for students and researchers in statistics and disciplines such as engineering, finance and environmental science, this book will also appeal to practitioners looking for practical help in solving real problems. Stuart Coles is Reader in Statistics at the University of Bristol, UK, having previously lectured at the universities of Nottingham and Lancaster. In 1992 he was the first recipient of the Royal Statistical Society's research prize. He has published widely in the statistical literature, principally in the area of extreme value modeling. |

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### Contents

Introduction | 1 |

Basics of Statistical Modeling | 18 |

Classical Extreme Value Theory and Models | 45 |

Threshold Models | 74 |

Extremes of Dependent Sequences | 92 |

Extremes of Nonstationary Sequences | 105 |

A Point Process Characterization of Extremes | 124 |

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analysis applied approach appropriate approximate arguments assumed asymptotic behavior bivariate block maxima Chapter choice cluster compared component confidence intervals corresponding daily defined denote density function dependence described discussed distribution function effect empirical errors example exceedances extreme value models FIGURE fitted follows GEV distribution GEV model give given Hence implies independent inference largest leads limit linear log-likelihood marginal maxima maximum likelihood estimate mean measure method multivariate normal observed obtained order statistic parameter particular period plot point process possible probability properties provides quantile plots random variables reasonable requires respectively return level return level plot sample scale sequence shape parameter shown similar Smith specified standard stationary statistic model statistical suggests Tawn techniques Theorem theory threshold excess tion trend usual valid variation vector