Symmetries of random discrete copulas

Arturo Erdely; José M. González–Barrios; Roger B. Nelsen

Kybernetika (2008)

  • Volume: 44, Issue: 6, page 846-863
  • ISSN: 0023-5954

Abstract

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In this paper we analyze some properties of the discrete copulas in terms of permutations. We observe the connection between discrete copulas and the empirical copulas, and then we analyze a statistic that indicates when the discrete copula is symmetric and obtain its main statistical properties under independence. The results obtained are useful in designing a nonparametric test for symmetry of copulas.

How to cite

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Erdely, Arturo, González–Barrios, José M., and Nelsen, Roger B.. "Symmetries of random discrete copulas." Kybernetika 44.6 (2008): 846-863. <http://eudml.org/doc/33969>.

@article{Erdely2008,
abstract = {In this paper we analyze some properties of the discrete copulas in terms of permutations. We observe the connection between discrete copulas and the empirical copulas, and then we analyze a statistic that indicates when the discrete copula is symmetric and obtain its main statistical properties under independence. The results obtained are useful in designing a nonparametric test for symmetry of copulas.},
author = {Erdely, Arturo, González–Barrios, José M., Nelsen, Roger B.},
journal = {Kybernetika},
keywords = {discrete copulas; r-symmetric permutations; independence; r-symmetric permutations; independence},
language = {eng},
number = {6},
pages = {846-863},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Symmetries of random discrete copulas},
url = {http://eudml.org/doc/33969},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Erdely, Arturo
AU - González–Barrios, José M.
AU - Nelsen, Roger B.
TI - Symmetries of random discrete copulas
JO - Kybernetika
PY - 2008
PB - Institute of Information Theory and Automation AS CR
VL - 44
IS - 6
SP - 846
EP - 863
AB - In this paper we analyze some properties of the discrete copulas in terms of permutations. We observe the connection between discrete copulas and the empirical copulas, and then we analyze a statistic that indicates when the discrete copula is symmetric and obtain its main statistical properties under independence. The results obtained are useful in designing a nonparametric test for symmetry of copulas.
LA - eng
KW - discrete copulas; r-symmetric permutations; independence; r-symmetric permutations; independence
UR - http://eudml.org/doc/33969
ER -

References

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  9. Mayor G., Suñer, J., Torrens J., 10.1109/TFUZZ.2006.882462, IEEE Trans. Fuzzy Systems 15 (2007), 410–416 DOI10.1109/TFUZZ.2006.882462
  10. Mesiar R., Discrete copulas – what they are, In: Joint EUSFLAT-LFA 2005, Conference Proceedings (E. Montseny and P. Sobrevilla, eds.) Universitat Politecnica de Catalunya, Barcelona 2005, pp. 927–930 
  11. Miller W., 10.2307/2322839, Amer. Math. Monthly 94 (1987), 6, 497–506 (1987) Zbl1191.11027MR0935414DOI10.2307/2322839
  12. Nelsen R. B., An Introduction to Copulas, Second edition. Springer, New York 2006 Zbl1152.62030MR2197664
  13. Schweizer B., Sklar A., Probabilistic Metric Spaces, North-Holland, New York 1983 Zbl0546.60010MR0790314
  14. Skiena S., The cycle structure of permutations, In: Implementing Discrete Mathematics: Combinatorial and Graph Theory with Mathematica. Addison-Wesley, Reading, MA 1990, pp. 20–24 (1990) MR1061378

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