Extreme Value Distributions
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Extreme Value Distributions
This important book provides an up-to-date comprehensive and down-to-earth survey of the theory and practice of extreme value distributions — one of the most prominent success stories of modern applied probability and statistics. Originated by E J Gumbel in the early forties as a tool for predicting floods, extreme value distributions evolved during the last 50 years into a coherent theory with applications in practically all fields of human endeavor where maximal or minimal values (the so-called extremes) are of relevance. The book is of usefulness both for a beginner with a limited probabilistic background and to expert in the field./a
Entropy-Based Parameter Estimation in Hydrology
Author: Vijay Singh
language: en
Publisher: Springer Science & Business Media
Release Date: 1998-10-31
Since the pioneering work of Shannon in the late 1940's on the development of the theory of entropy and the landmark contributions of Jaynes a decade later leading to the development of the principle of maximum entropy (POME), the concept of entropy has been increasingly applied in a wide spectrum of areas, including chemistry, electronics and communications engineering, data acquisition and storage and retreival, data monitoring network design, ecology, economics, environmental engineering, earth sciences, fluid mechanics, genetics, geology, geomorphology, geophysics, geotechnical engineering, hydraulics, hydrology, image processing, management sciences, operations research, pattern recognition and identification, photogrammetry, psychology, physics and quantum mechanics, reliability analysis, reservoir engineering, statistical mechanics, thermodynamics, topology, transportation engineering, turbulence modeling, and so on. New areas finding application of entropy have since continued to unfold. The entropy concept is indeed versatile and its applicability widespread. In the area of hydrology and water resources, a range of applications of entropy have been reported during the past three decades or so. This book focuses on parameter estimation using entropy for a number of distributions frequently used in hydrology. In the entropy-based parameter estimation the distribution parameters are expressed in terms of the given information, called constraints. Thus, the method lends itself to a physical interpretation of the parameters. Because the information to be specified usually constitutes sufficient statistics for the distribution under consideration, the entropy method provides a quantitative way to express the information contained in the distribution.
Extreme Value Theory
Author: Laurens de Haan
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-12-09
Extreme Value Theory offers a careful, coherent exposition of the subject starting from the probabilistic and mathematical foundations and proceeding to the statistical theory. The book covers both the classical one-dimensional case as well as finite- and infinite-dimensional settings. All the main topics at the heart of the subject are introduced in a systematic fashion so that in the final chapter even the most recent developments in the theory can be understood. The treatment is geared toward applications. The presentation concentrates on the probabilistic and statistical aspects of extreme values such as limiting results, domains of attraction and development of estimators without emphasizing related topics such as point processes, empirical distribution functions and Brownian motion. An appendix on regular variation has been added since some required results in that area are not available in book form. The usefulness of the statistical theory is shown by treating several case studies in detail. The book is a thorough, accessible, self-contained, graduate level treatment of modern extreme value theory and some of its applications. It is aimed at graduate students and researchers and requires only maturity in mathematics and statistics.