Band copulas as spectral measures for two-dimensional stable random vectors

Jacek Bojarski; Jolanta K. Misiewicz

Discussiones Mathematicae Probability and Statistics (2003)

  • Volume: 23, Issue: 1, page 69-75
  • ISSN: 1509-9423

Abstract

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In this paper, we study basic properties of symmetric stable random vectors for which the spectral measure is a copula, i.e., a distribution having uniformly distributed marginals.

How to cite

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Jacek Bojarski, and Jolanta K. Misiewicz. "Band copulas as spectral measures for two-dimensional stable random vectors." Discussiones Mathematicae Probability and Statistics 23.1 (2003): 69-75. <http://eudml.org/doc/287750>.

@article{JacekBojarski2003,
abstract = {In this paper, we study basic properties of symmetric stable random vectors for which the spectral measure is a copula, i.e., a distribution having uniformly distributed marginals.},
author = {Jacek Bojarski, Jolanta K. Misiewicz},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {Symmetric stable random vector; spectral measure; canonical spectral measure; copula; James corelation for random variables; James correlation for random variables},
language = {eng},
number = {1},
pages = {69-75},
title = {Band copulas as spectral measures for two-dimensional stable random vectors},
url = {http://eudml.org/doc/287750},
volume = {23},
year = {2003},
}

TY - JOUR
AU - Jacek Bojarski
AU - Jolanta K. Misiewicz
TI - Band copulas as spectral measures for two-dimensional stable random vectors
JO - Discussiones Mathematicae Probability and Statistics
PY - 2003
VL - 23
IS - 1
SP - 69
EP - 75
AB - In this paper, we study basic properties of symmetric stable random vectors for which the spectral measure is a copula, i.e., a distribution having uniformly distributed marginals.
LA - eng
KW - Symmetric stable random vector; spectral measure; canonical spectral measure; copula; James corelation for random variables; James correlation for random variables
UR - http://eudml.org/doc/287750
ER -

References

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  1. [1] J. Bojarski, A new class of band copulaes - distributions with uniform marginals, preprint (2001). 
  2. [2] T.S. Ferguson, A class of symmetric bivariate uniform distributions, Statist. Papers 36, (1995). Zbl0817.62040
  3. [3] E. Feldheim, Etude de la stabilité de lois de probabilité, Ph. Thesis, Thése de la Faculté des sciences de Paris 1937. Zbl62.1347.01
  4. [4] M. Ledoux and M. Talagrand, Probability in Banach spaces, Isoperymetry and Processes, A series of Modern Surveys in Mathematics, Springer Verlag, band 23 (1991). 
  5. [5] P. Lévy, Théorie de l'addition des variables aléatoires, 2nd edn, Gauthier-Villars, Paris 1954. Zbl0056.35903
  6. [6] Nelsen R. B, An Introduction to Copulas, John Wiley & Sons, New York 1999. Zbl0909.62052
  7. [7] D. Kurowicka and R. Cooke, Conditional and partial correlation for graphical uncertainty model, Proceedings of the 2nd International Conference on Mathematical Methods in Reliability, Recent Advences in Reliability Theory, Birkhäuser 2000, 259-276. Zbl0957.62086
  8. [8] G. Samorodnitsky and M. Taqqu, Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance, Chapman & Hall, London 1993. Zbl0925.60027

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