Skip to main content

Representation of Exchangeable Sequences by Means of Copulas

  • Conference paper
Combining Soft Computing and Statistical Methods in Data Analysis

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 77))

  • 1601 Accesses

Abstract

Given a sequence \(\mathbf X=(X_n)_{n\in \mathbb N}\) of exchangeable continuous random variables, it is proved that the joint distribution function of every finite subset of random variables belonging to X is fully described by means of a suitable bivariate copula and a univariate distribution function.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Albanese, A., Sempi, C.: Countably generated idempotent copulas. In: Soft methodology and random information systems, Adv. Soft Comput., pp. 197–204. Springer, Berlin (2004)

    Google Scholar 

  2. Aldous, D.J.: Exchangeability and related topics. In: École d’été de probabilités de Saint-Flour, XIII—1983. Lecture Notes in Math., vol. 1117, pp. 1–198. Springer, Berlin (1985)

    Google Scholar 

  3. Angus, J.E.: The probability integral transform and related results. SIAM Rev. 36(4), 652–654 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cuadras, C.M., Augé, J.: A continuous general multivariate distribution and its properties. Comm. Statist. A—Theory Methods 10(4), 339–353 (1981)

    Article  MathSciNet  Google Scholar 

  5. Darsow, W.F., Nguyen, B., Olsen, E.T.: Copulas and Markov processes. Illinois J. Math. 36(4), 600–642 (1992)

    MATH  MathSciNet  Google Scholar 

  6. Durante, F., Quesada-Molina, J.J., Úbeda-Flores, M.: On a family of multivariate copulas for aggregation processes. Inform. Sci. 177(24), 5715–5724 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  7. Durrett, R.: Probability: theory and examples, 2nd edn. Duxbury Press, Belmont (1996)

    Google Scholar 

  8. Hu, T.C.: On pairwise independent and independent exchangeable random variables. Stochastic Anal. Appl. 15(1), 51–57 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  9. Jaworski, P., Durante, F., Härdle, W., Rychlik, T. (eds.): Copula Theory and its Applications. Lecture Notes in Statistics - Proceedings. Springer, Dortrecht (2010)

    MATH  Google Scholar 

  10. Joe, H.: Multivariate models and dependence concepts. Monographs on Statistics and Applied Probability, vol. 73. Chapman & Hall, London (1997)

    MATH  Google Scholar 

  11. Kallenberg, O.: Probabilistic symmetries and invariance principles. In: Probability and its Applications. Springer, New York (2005)

    Google Scholar 

  12. Lagerås, A.N.: Copulas for Markovian dependence. Bernoulli (in press, 2010)

    Google Scholar 

  13. Mai, J.F., Scherer, M.: Lévy-Frailty copulas. J. Multivariate Anal. 100(7), 1567–1585 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  14. McNeil, A.J., Frey, R., Embrechts, P.: Quantitative risk management. Concepts, techniques and tools. Princeton Series in Finance. Princeton University Press, Princeton (2005)

    MATH  Google Scholar 

  15. Nelsen, R.B.: An introduction to copulas, 2nd edn. Springer Series in Statistics. Springer, New York (2006)

    MATH  Google Scholar 

  16. Olshen, R.: A note on exchangable sequences. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 28, 317–321 (1973/1974)

    Google Scholar 

  17. Rogers, L.C.G., Williams, D.: Diffusions, Markov processes, and martingales. Cambridge Mathematical Library, vol. 1. Cambridge University Press, Cambridge (2000), (Foundations, Reprint of the second (1994) edition)

    Google Scholar 

  18. Scarsini, M., Verdicchio, L.: On the extendibility of partially exchangeable random vectors. Statist. Probab. Lett. 16(1), 43–46 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  19. Sklar, A.: Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8, 229–231 (1959)

    MathSciNet  Google Scholar 

  20. Spizzichino, F.: Extendibility of symmetric probability distributions and related bounds. In: Exchangeability in probability and statistics, Rome, pp. 313–320. North-Holland, Amsterdam (1981/1982)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Durante, F., Mai, JF. (2010). Representation of Exchangeable Sequences by Means of Copulas. In: Borgelt, C., et al. Combining Soft Computing and Statistical Methods in Data Analysis. Advances in Intelligent and Soft Computing, vol 77. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14746-3_28

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14746-3_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14745-6

  • Online ISBN: 978-3-642-14746-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics