Stuart Coles' "An Introduction to Statistical Modeling of Extreme Values" is a comprehensive textbook on extreme value theory. The book provides a statistical perspective on the modeling of extreme events, which are rare occurrences that can have significant impacts. It is aimed at both statisticians and non-statisticians, with a focus on practical applications in fields such as civil engineering, oceanography, wind engineering, and finance.
The book begins with an introduction to extreme value theory, its historical development, and the importance of modeling extreme events. It then covers the basics of statistical modeling, including random variables, distributions, and limit laws. The core of the book is devoted to classical extreme value theory, including block maxima models, threshold exceedance models, and extensions to stationary and non-stationary sequences. It also introduces point process modeling and multivariate extreme value models.
The text includes numerous examples and datasets from various fields, illustrating the application of extreme value models. It emphasizes the use of likelihood-based methods for inference, which allow for the incorporation of all relevant information and the quantification of uncertainties in estimation. The book also discusses more advanced topics such as Bayesian inference and spatial extremes.
The book is based on introductory courses given at several universities and is written with a clear and accessible style. It is intended to be a practical guide for practitioners of extreme value modeling, with a focus on real-world applications. The mathematical level is elementary, and detailed mathematical proofs are often replaced by heuristic arguments. The book is supported by the S-PLUS statistical software program, with corresponding datasets and functions available online.Stuart Coles' "An Introduction to Statistical Modeling of Extreme Values" is a comprehensive textbook on extreme value theory. The book provides a statistical perspective on the modeling of extreme events, which are rare occurrences that can have significant impacts. It is aimed at both statisticians and non-statisticians, with a focus on practical applications in fields such as civil engineering, oceanography, wind engineering, and finance.
The book begins with an introduction to extreme value theory, its historical development, and the importance of modeling extreme events. It then covers the basics of statistical modeling, including random variables, distributions, and limit laws. The core of the book is devoted to classical extreme value theory, including block maxima models, threshold exceedance models, and extensions to stationary and non-stationary sequences. It also introduces point process modeling and multivariate extreme value models.
The text includes numerous examples and datasets from various fields, illustrating the application of extreme value models. It emphasizes the use of likelihood-based methods for inference, which allow for the incorporation of all relevant information and the quantification of uncertainties in estimation. The book also discusses more advanced topics such as Bayesian inference and spatial extremes.
The book is based on introductory courses given at several universities and is written with a clear and accessible style. It is intended to be a practical guide for practitioners of extreme value modeling, with a focus on real-world applications. The mathematical level is elementary, and detailed mathematical proofs are often replaced by heuristic arguments. The book is supported by the S-PLUS statistical software program, with corresponding datasets and functions available online.