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2013 | OriginalPaper | Buchkapitel

4. A Structural Classification of Probability Distances

verfasst von : Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov, Frank J. Fabozzi

Erschienen in: The Methods of Distances in the Theory of Probability and Statistics

Verlag: Springer New York

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Abstract

The goals of this chapter are to: Introduce and motivate three classifications of probability metrics according to their metric structure, Provide examples of probability metrics belonging to a particular structural group, Discuss the generic properties of the structural groups and the links between them.

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Fußnoten
1
The proof of (4.2.14) is quite analogous to that given in Hennequin and Tortrat (1965, Chap.​ 19), for the case \(\lambda = 1\).
 
2
See (4.2.5) and subsequently Corollary 7.4.2 and (7.5.15) in Chap.​ 7.
 
3
See Billingsley [1999, Theorem 14.2].
 
4
See Billingsley [1999, Sect. 12].
 
5
See Rachev [1984] and Kakosyan et al. [1988, Sect. 2.5].
 
6
See Dudley [1976, Theorem 8.1].
 
7
See Prokhorov [1956] and Dudley [2002, Theorem 11.3.3].
 
8
See, for instance, Sazonov [1981] and Senatov [1980].
 
9
See Bhattacharya and Ranga Rao [1976] and Ranga [1962].
 
10
See Dudley [1966].
 
11
See Zolotarev [1976, 1977, 1978] and Hall [1981].
 
12
See Neveu and Dudley [1980].
 
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Metadaten
Titel
A Structural Classification of Probability Distances
verfasst von
Svetlozar T. Rachev
Lev B. Klebanov
Stoyan V. Stoyanov
Frank J. Fabozzi
Copyright-Jahr
2013
Verlag
Springer New York
DOI
https://doi.org/10.1007/978-1-4614-4869-3_4