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The Methods of Distances in the Theory of Probability and Statistics

Author: Svetlozar T Rachev; Lev B Klebanov; Stoyan V Stoyanov; Frank Fabozzi
Publisher: New York, NY : Springer New York : Imprint: Springer, 2013.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
This book covers the method of metric distances and its application in probability theory and other fields. The method is fundamental in the study of limit theorems and generally in assessing the quality of approximations to a given probabilistic model. The method of metric distances is developed to study stability problems and reduces to the selection of an ideal or the most appropriate metric for the problem  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Svetlozar T Rachev; Lev B Klebanov; Stoyan V Stoyanov; Frank Fabozzi
ISBN: 9781461448693 1461448697
OCLC Number: 841812305
Description: 1 online resource (XVI, 619 p. 17 illus.)
Contents: Main directions in the theory of probability metrics --
Probability distances and probability metrics: Definitions --
Primary, simple and compound probability distances, and minimal and maximal distances and norms --
A structural classification of probability distances.-Monge-Kantorovich mass transference problem, minimal distances and minimal norms --
Quantitative relationships between minimal distances and minimal norms --
K-Minimal metrics --
Relations between minimal and maximal distances --
Moment problems related to the theory of probability metrics: Relations between compound and primary distances --
Moment distances --
Uniformity in weak and vague convergence --
Glivenko-Cantelli theorem and Bernstein-Kantorovich invariance principle --
Stability of queueing systems.-Optimal quality usage --
Ideal metrics with respect to summation scheme for i.i.d. random variables --
Ideal metrics and rate of convergence in the CLT for random motions --
Applications of ideal metrics for sums of i.i.d. random variables to the problems of stability and approximation in risk theory --
How close are the individual and collective models in risk theory?- Ideal metric with respect to maxima scheme of i.i.d. random elements --
Ideal metrics and stability of characterizations of probability distributions --
Positive and negative de nite kernels and their properties --
Negative definite kernels and metrics: Recovering measures from potential --
Statistical estimates obtained by the minimal distances method --
Some statistical tests based on N-distances --
Distances defined by zonoids --
N-distance tests of uniformity on the hypersphere.-.
Responsibility: by Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank Fabozzi.

Abstract:

This book covers the method of metric distances and its application in probability theory and other fields. Its presentation offers specific cases as they arise in the process of finding  Read more...

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