The methods of distances in the theory of probability and statistics /

The methods of distances in the theory of probability and statistics / Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi.

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...

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Bibliographic Details
Online Access: Full Text (via Springer)
Other Authors: Rachev, S. T. (Svetlozar Todorov), Klebanov, Lev B., Stoyanov, Stoyan V., Fabozzi, Frank
Format: eBook
Language:English
Published: New York ; London : Springer, ©2013.
Subjects:
Mathematics.
Distribution (Probability theory)
Mathematical statistics.
Table of 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.-

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