Skip to main content
Springer Nature Link
Log in

On a family of copulas constructed from the diagonal section

  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

We characterize the class of copulas that can be constructed from the diagonal section by means of the functional equation C(x,y)+|x−y|=C(x∨y,x∨y), for all (x,y) in the unit square such that C(x,y)>0. Some statistical properties of this class are given.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Alsina C, Nelsen RB, Schweizer B (1993) On the characterization of a class of binary operations on distribution functions. Statist Probab Lett 17:85–89

    Google Scholar 

  2. Calvo T, Kolesárová A, Komorníková 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, Heidelberg, pp 3–106

  3. Bassan B, Spizzichino F (2005) Relations among univariate aging, bivariate aging and dependence for exchangeable lifetimes. J Multivar Anal 93: 313–339

    Google Scholar 

  4. Bertino S (1977) Sulla dissomiglianza tra mutabili cicliche. Metron 35:53–88

    Google Scholar 

  5. Durante F, Sempi C (2005) Semicopulæ. Kybernetika 41: 315–328

    Google Scholar 

  6. Dunford N, Schwartz JT (1958) Linear operators. Part I: General theory. Wiley, New York

  7. Fredricks GA, Nelsen RB (1997) Copulas constructed from diagonal sections. In: Beneš V, Štěpán J (eds), Distributions with given marginals and moment problems. Kluwer, Dordrecht, pp 129–136

  8. Fredricks GA, Nelsen RB (2003) The Bertino family of copulas. In: Cuadras CM, Fortiana J, Rodrí guez Lallena JA (eds), Distributions with given marginals and Statistical Modelling. Kluwer, Dordrecht, pp 81–91

  9. Genest C, Quesada Molina JJ, Rodríguez Lallena JA, Sempi C (1999) A characterization of quasi-copulas. J Multivar Anal 69:193–205

  10. Klement EP, Kolesárová A (2004) 1–Lipschitz aggregation operators, quasi–copulas and copulas with given diagonals. In: López Diaz M, Gil MA, Grzegorzewski P, Hryniewicz O, Lawry J (eds), Soft methodology and random information systems, advances in soft computing, pp 205–211

  11. Klement EP, Kolesárová A (2005) Extension to copulas and quasi-copulas as special 1-Lipschitz aggregation operators. Kybernetika 41, no. 3

    Google Scholar 

  12. Klement EP, Mesiar R, Pap E (2000) Triangular norms. Kluwer, Dordrecht

  13. Klement EP, Mesiar R, Pap E (2002) Invariant copulas. Kybernetika 38:275–285

    Google Scholar 

  14. Klement EP, Mesiar R, Pap E (2004) Measure-based aggregation operators. Fuzzy Sets Syst 142:3–14

    Google Scholar 

  15. Mayor G, Torrens J (1991) On a family of t–norms. Fuzzy Sets Syst 41:161–166

    Google Scholar 

  16. Nelsen RB, Fredricks GA (1997) Diagonal copulas. In: Beneš V, Štěpán J (eds), Distributions with given marginals and moment problems. Kluwer, Dordrecht, pp 121–128

  17. Nelsen RB (1999) An introduction to copulas. Lecture Notes in Statistics. Springer, New York

  18. Nelsen RB, Quesada Molina JJ, Rodrí guez Lallena JA, Úbeda Flores M (2004) Best–possible bounds on sets of bivariate distribution functions. J Multivar Anal 90:348–358

  19. Schweizer B, Sklar A (1983) Probabilistic metric spaces. Elsevier, New York

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica “Ennio De Giorgi”, Università di Lecce, Lecce, 73100, Italy

    F. Durante & C. Sempi

  2. Stu Bratislava, Radlinskeho 11, 813 68, Bratislava, Slovakia

    R. Mesiar

  3. Utia Av Cr, P.O. box 18, 18208, Prague, Czech Republic

    R. Mesiar

Authors
  1. F. Durante
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. R. Mesiar
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. C. Sempi
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to C. Sempi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Durante, F., Mesiar, R. & Sempi, C. On a family of copulas constructed from the diagonal section. Soft Comput 10, 490–494 (2006). https://doi.org/10.1007/s00500-005-0523-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-005-0523-7

Mathematics Subject Classification

Keywords