Discussiones Mathematicae Probability and Statistics 23(1) (2003) 69-75

BAND COPULAS AS SPECTRAL MEASURES FOR TWO-DIMENSIONAL STABLE RANDOM VECTORS

Jacek Bojarski and Jolanta K. Misiewicz

Institute of Mathematics University of Zielona Góra
Podgórna 50, 65-246 Zielona Góra, Poland
e-mail: j.bojarski@im.uz.zgora.pl
e-mail: j.misiewicz@im.uz.zgora.pl  

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.

Keywords: Symmetric stable random vector, spectral measure, canonical spectral measure, copula, James corelation for random variables.

2000 Mathematics Subject Classification: 60A99, 60E07, 60E10, 60E99.

References

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

Received 10 March 2003