Statistical Techniques for Modelling Extreme Value Data and Related Applications

This book tackles some modern trends and methods in the modelling of extreme data. Usually such data arise from random phenomena such as floods, hurricanes, air and water pollutants, extreme claim sizes, life spans, and maximum sizes of ecological populations. It provides the latest statistical methods to model these random phenomena to understand and predict them, thus allowing the avoidance of damage or at least minimizing it. In addition, this book sheds light on the mathematical and statistical theories on which applied modelling methods were built. Therefore, it has both an applied and theoretical orientation, and represents a valuable addition to existing literature on the modelling of extreme value data. Contents Preface Notations and abbreviations List of illustrations List of tables 1 Introduction: Some basic and miscellaneous results 2 Asymptotic theory of order statistics: A historical retrospective 3 Bootstrap order statistics and calibration of the sub-sample bootstrap method 4 Statistical modelling of extreme value data under linear normalization 5 Extreme value modelling under power normalization 6 Methods of threshold selection 7 Estimations under power normalization for the EVI 8 Some applications to real data examples 9 Miscellaneous results Appendix A: Summary of Hill’s estimators in the L-model and P-model References Author index Subject index