This book is designed as a unified and mathematically rigorous treatment of some recent developments of the asymptotic distribution theory of order statistics (including the extreme order statistics) that are relevant for statistical theory and its applications. Particular emphasis is placed on results concern ing the accuracy oflimit theorems, on higher order approximations, and other approximations in quite a general sense. Contrary to the classical limit theorems that primarily concern the weak convergence of distribution functions, our main results will be formulated in terms of the variational and the Hellinger distance. These results will form the proper springboard for the investigation of parametric approximations of nonparametric models of joint distributions of order statistics. The approxi mating models include normal as well as extreme value models. Several applications will show the usefulness of this approach. Other recent developments in statistics like nonparametric curve estima tion and the bootstrap method will be studied as far as order statistics are concerned. 1n connection with this, graphical methods will, to some extent, be explored.

Approximate Distributions of Order Statistics: With Applications to Nonparametric Statistics (Springer Series in Statistics)

Science & Math

Reiss, Rolf-Dieter

Mathematics

Springer

The mathematical theory and applications of extremes and rare events have developed much since this book was first published in 1994. This third edition includes details of multivariate generalized Pareto distributions and their testing and estimation.

Laws of Small Numbers: Extremes and Rare Events

FALK, MICHAEL

Hüsler, Jürg

Birkhauser

Provides broad statistical background as well as instruction in the statistical analysis of extreme values. Includes special chapters about flood frequency analysis, insurance, and finance. The CD-ROM offers a 32-bit statistical software called Xtremes. System requirements not listed. Softcover.

Statistical Analysis of Extreme Values: with Applications to Insurance, Finance, Hydrology and Other Fields

Thomas, Michael

Evolution

Statistical analysis of extreme data is vital to many disciplines including hydrology, insurance, finance, engineering and environmental sciences. This book provides a self-contained introduction to parametric modeling, exploratory analysis and statistical interference for extreme values. For this Third Edition, the entire text has been thoroughly updated and rearranged to meet contemporary requirements, with new sections and chapters address such topics as dependencies, the conditional analysis and the multivariate modeling of extreme data. New chapters include An Overview of Reduced-Bias Estimation; The Spectral Decomposition Methodology; About Tail Independence; and Extreme Value Statistics of Dependent Random Variables.

Business & Money

Economics

See the best price to sell, buy, or rent books by Reiss, Rolf-Dieter. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Reiss, Rolf-Dieter