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The Methods of Distances in the Theory of Probability and Statistics

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Cover of 'The Methods of Distances in the Theory of Probability and Statistics'

Table of Contents

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    Book Overview
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    Chapter 1 Main Directions in the Theory of Probability Metrics
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    Chapter 2 Probability Distances and Probability Metrics: Definitions
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    Chapter 3 Primary, Simple, and Compound Probability Distances and Minimal and Maximal Distances and Norms
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    Chapter 4 A Structural Classification of Probability Distances
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    Chapter 5 Monge–Kantorovich Mass Transference Problem, Minimal Distances and Minimal Norms
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    Chapter 6 Quantitative Relationships Between Minimal Distances and Minimal Norms
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    Chapter 7 K -Minimal Metrics
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    Chapter 8 Relations Between Minimal and Maximal Distances
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    Chapter 9 Moment Problems Related to the Theory of Probability Metrics: Relations Between Compound and Primary Distances
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    Chapter 10 Moment Distances
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    Chapter 11 Uniformity in Weak and Vague Convergence
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    Chapter 12 Glivenko–Cantelli Theorem and Bernstein–Kantorovich Invariance Principle
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    Chapter 13 Stability of Queueing Systems
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    Chapter 14 Optimal Quality Usage
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    Chapter 15 Ideal Metrics with Respect to Summation Scheme for i.i.d. Random Variables
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    Chapter 16 Ideal Metrics and Rate of Convergence in the CLT for Random Motions
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    Chapter 17 Applications of Ideal Metrics for Sums of i.i.d. Random Variables to the Problems of Stability and Approximation in Risk Theory
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    Chapter 18 How Close Are the Individual and Collective Models in Risk Theory?
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    Chapter 19 Ideal Metric with Respect to Maxima Scheme of i.i.d. Random Elements
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    Chapter 20 Ideal Metrics and Stability of Characterizations of Probability Distributions
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    Chapter 21 Positive and Negative Definite Kernels and Their Properties
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    Chapter 22 Negative Definite Kernels and Metrics: Recovering Measures from Potentials
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    Chapter 23 Statistical Estimates Obtained by the Minimal Distances Method
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    Chapter 24 Some Statistical Tests Based on $$\mathfrak{N}$$ -Distances
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    Chapter 25 Distances Defined by Zonoids
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    Chapter 26 $$\mathfrak{N}$$ -Distance Tests of Uniformity on the Hypersphere
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Title
The Methods of Distances in the Theory of Probability and Statistics
Published by
Springer-Verlag New York, January 2013
DOI 10.1007/978-1-4614-4869-3
ISBNs
978-1-4614-4869-3, 978-1-4614-4868-6, 978-1-4899-9569-8
Authors

Svetlozar T. Rachev, Lev Klebanov, Stoyan V. Stoyanov, Frank Fabozzi, Rachev, Svetlozar T., Klebanov, Lev B., Stoyanov, Stoyan V., Fabozzi, Frank

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Mendeley readers

Mendeley readers

The data shown below were compiled from readership statistics for 93 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
United States 2 2%
Poland 1 1%
France 1 1%
Unknown 89 96%

Demographic breakdown

Readers by professional status Count As %
Student > Ph. D. Student 29 31%
Researcher 15 16%
Student > Master 12 13%
Professor > Associate Professor 7 8%
Student > Doctoral Student 4 4%
Other 12 13%
Unknown 14 15%
Readers by discipline Count As %
Mathematics 19 20%
Computer Science 17 18%
Physics and Astronomy 11 12%
Engineering 11 12%
Business, Management and Accounting 4 4%
Other 13 14%
Unknown 18 19%