## 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

I | 2 |

II | 5 |

III | 14 |

IV | 17 |

V | 19 |

VIII | 20 |

X | 22 |

XI | 23 |

LXIII | 94 |

LXIV | 98 |

LXV | 99 |

LXVII | 101 |

LXVIII | 104 |

LXIX | 105 |

LXX | 106 |

LXXIII | 109 |

XII | 26 |

XIII | 27 |

XIV | 28 |

XVI | 29 |

XVII | 31 |

XVIII | 32 |

XIX | 34 |

XX | 35 |

XXI | 37 |

XXII | 39 |

XXIII | 44 |

XXIV | 46 |

XXVII | 47 |

XXVIII | 48 |

XXIX | 50 |

XXX | 52 |

XXXI | 53 |

XXXII | 55 |

XXXIV | 56 |

XXXV | 57 |

XXXVI | 58 |

XXXVIII | 60 |

XL | 65 |

XLI | 67 |

XLIII | 69 |

XLIV | 70 |

XLV | 73 |

XLVI | 75 |

XLIX | 76 |

LI | 77 |

LII | 78 |

LIII | 79 |

LIV | 81 |

LV | 82 |

LVI | 84 |

LVII | 85 |

LVIII | 87 |

LIX | 91 |

LX | 93 |

LXXV | 110 |

LXXVI | 111 |

LXXVII | 112 |

LXXVIII | 115 |

LXXIX | 118 |

LXXX | 120 |

LXXXI | 123 |

LXXXII | 125 |

LXXXVI | 129 |

LXXXVIII | 131 |

LXXXIX | 132 |

XC | 133 |

XCI | 135 |

XCII | 137 |

XCIII | 138 |

XCIV | 142 |

XCV | 143 |

XCVII | 144 |

XCVIII | 148 |

XCIX | 149 |

C | 151 |

CI | 154 |

CII | 155 |

CIII | 157 |

CIV | 159 |

CV | 164 |

CVI | 168 |

CVII | 170 |

CXI | 173 |

CXII | 174 |

CXIII | 178 |

CXIV | 180 |

CXV | 182 |

CXVI | 183 |

CXVII | 186 |

196 | |

206 | |

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### Common terms and phrases

100-year return level analysis annual maximum sea-level applications approximate arguments asymptotic Bayesian behavior block maxima Chapter choice cluster component confidence intervals corresponding daily rainfall data of Example delta method denote dependence deviance statistic diagnostic plots distribution function exceedances extrapolation extreme value distribution extreme value models extreme value theory FIGURE Fremantle GEV distribution GEV family GEV model Gumbel inference largest order statistic leads likelihood function limit distribution log-daily returns marginal distribution Markov chain maximized log-likelihood maximum likelihood estimate model fitted multivariate extremes non-stationarity observed obtained order statistic model parameter estimates Pareto distribution point process model Poisson process Port Pirie probability plot profile likelihood provides quantile plots random variables reasonable return level plot Return Period S-PLUS sample scale sequence of independent shape parameter shown in Fig standard errors standard Frechet stationary series Tawn techniques temperature series Theorem threshold excess model tion univariate variance-covariance matrix vector Wooster temperature

### Popular passages

Page 196 - Beirlant, J., Vynckier, P. and Teugels, JL (1996). Tail index estimation, Pareto quantile plots and regression diagnostics, J.

Page 200 - Families of min-stable multivariate exponential and multivariate extreme value distributions. Statistics and Probability Letters 9, 75-81. JOE, H. (1994). Multivariate extreme value distributions with applications to environmental data.

Page viii - As an abstract study of random phenomena, the subject can be traced back to the early part of the 20th century. It was not until the 1950's that the methodology was proposed in any serious way for the modeling of genuine physical phenomena.

Page 196 - BARNETT, V. (1976). The ordering of multivariate data (with discussion). Journal of the Royal Statistical Society, A 139, 318-355.

Page 203 - Extreme value analysis of environmental time series: An example based on ozone data (with Discussion).