Statistical Papers

, Volume 50, Issue 2, pp 383–391 | Cite as

Construction of non-exchangeable bivariate distribution functions

Note

Abstract

A method is given for constructing bivariate distributions functions by means of the copula functions, and, hence, it is used for obtaining distribution functions that can describe the behaviour of non–exchangeable random vectors.

Keywords

Bivariate distribution function Copula Exchangeability 

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References

  1. Calvo T, Kolesárová A, Komorní ková M, Mesiar R (2002) Aggregation operators: properties, classes and construction methods. In: Calvo T, Mesiar R, Mayor G (eds) Aggregation operators. New trends and applications. Physica-Verlag, Heidelberg, pp 3–106Google Scholar
  2. Cherubini U, Luciano E, Vecchiato W (2004) Copula methods in finance. Wiley, New YorkMATHGoogle Scholar
  3. Durante F (2005) Generalized composition of binary aggregation operators. Int J Uncertain Fuzziness Knowl Based Syst 13:567–577MATHCrossRefMathSciNetGoogle Scholar
  4. Durante F, Sempi C (2005) Copula and semicopula transforms. Int J Math Math Sci 2005:645–655MATHCrossRefMathSciNetGoogle Scholar
  5. Durante F, Sempi C (2006) On the characterization of a class of binary operations on bivariate distribution functions. Publ Math Debr 69:47–63MATHMathSciNetGoogle Scholar
  6. Durante F, Mesiar R, Papini PL, Sempi C (2007) 2-increasing binary aggregation operators. Inform Sci 177:111–129MATHCrossRefMathSciNetGoogle Scholar
  7. Frees EW, Valdez EA (1998) Understanding relationships usingcopulas. North Am Act J 2:1–25MATHMathSciNetGoogle Scholar
  8. Genest C, Favre A-C (2007) Everything you always wanted to know about copula modeling but were afraid to ask. J Hydrol Eng 12 (in press)Google Scholar
  9. Genest C, MacKay RJ (1986) Copules archimédiennes et familles de lois bidimensionnelles dont les marges sont données. Can J Stat 14:145–159MATHCrossRefMathSciNetGoogle Scholar
  10. Genest C, Ghoudi K, Rivest L-P (1998) Discussion on the paper Understanding relationships using copulas by Frees E.W., Valdez E.A. North Am Act J 2:143–149Google Scholar
  11. Hutchinson TP, Lai CD (1990) Continuous bivariate distributions. Emphasising applications. Rumsby Scientific Publishing, AdelaideGoogle Scholar
  12. Joe H (1997) Multivariate models and dependence concepts. Chapman & Hall, LondonMATHGoogle Scholar
  13. Klement EP, Mesiar R, Pap E (2005) Archimax copulas and invariance under transformations. CR Math Acad Sci Paris 240:755–758MathSciNetGoogle Scholar
  14. McNeil AJ, Frey R, Embrechts P (2005) Quantitative risk management concepts, techniques and tools Princeton Series in Finance. Princeton University Press, PrincetonGoogle Scholar
  15. Morillas PM (2005) A method to obtain new copulas from a given one. Metrika 61:169–184MATHCrossRefMathSciNetGoogle Scholar
  16. Müller A, Scarsini M (2001) Stochastic comparison of random vectors with a common copula. Math Oper Res 26:723–740MATHCrossRefMathSciNetGoogle Scholar
  17. Nelsen RB (2006) An introduction to copulas. Springer, HeidelbergMATHGoogle Scholar
  18. Nelsen RB (2007) Extremes of nonexchangeability. Stat Pap 48:329–336MATHCrossRefMathSciNetGoogle Scholar
  19. Shaked M, Shanthikumar JG (1990) Parametric stochastic convexity and concavity of stochastic processes. Ann Inst Stat Math 42:509–531MATHCrossRefMathSciNetGoogle Scholar
  20. Tawn JA (1988) Bivariate extreme value theory: models and estimation. Biometrika 75:397–415MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Knowledge-Based Mathematical SystemsJohannes Kepler UniversityLinzAustria

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