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An extension of the Gumbel–Barnett family of copulas

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Abstract

The Gumbel–Barnett family of bivariate distributions with given marginals, is frequently used in theory and applications. This family has been generalized in several ways. We propose and study a broad generalization by using two differentiable functions. We obtain some properties and describe particular cases.

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References

  • Bekrizadeh H, Parham G, Jamshidi B (2017) A new asymmetric class of bivariate copulas for modeling dependence. Commun Stat Simul Comput 46(7):5594–5609

    Article  MathSciNet  Google Scholar 

  • Celebioglu S (1997) A way of generating comprehensive copulas. J Inst Sci Technol 10(1):57–61

    Google Scholar 

  • Cuadras CM (2002) On the covariance between functions. J Multivar Anal 81(1):19–27

    Article  MathSciNet  Google Scholar 

  • Cuadras CM (2006) The importance of being the upper bound in the bivariate family. SORT 30(1):55–84

    MathSciNet  MATH  Google Scholar 

  • Cuadras CM (2009) Constructing copula functions with weighted geometric means. J Stat Plan Infer 139(11):3766–3772

    Article  MathSciNet  Google Scholar 

  • Cuadras CM (2015) Contributions to the diagonal expansion of a bivariate copula with continuous extensions. J Multivar Anal 139:28–44

    Article  MathSciNet  Google Scholar 

  • Cuadras CM, Diaz W (2012) Another generalization of the bivariate FGM distribution with two-dimensional extensions. Acta Comment Univ Tartu Math 16(1):3–12

    MathSciNet  MATH  Google Scholar 

  • Cuadras CM, Diaz W, Salvo-Garrido S (2020) Two generalized bivariate FGM distributions and rank reduction. Commun Stat Theory Methods 49(23):5639–5665

    Article  MathSciNet  Google Scholar 

  • Diaz W, Cuadras CM (2017) On a multivariate generalization of the covariance. Commun Stat Theory Methods 46(9):4660–4669

    Article  MathSciNet  Google Scholar 

  • Durante F, Sempi C (2016) Principles of copula theory, vol 474. CRC Press, Boca Raton, FL

    MATH  Google Scholar 

  • Hutchinson T, Lai C (1991) The engineering statistician’s guide to continuous bivariate distributions. Rumsby Scientific Pub

  • Joe H (1997) Multivariate models and dependence concepts. Chapman & Hall/CRC Monographs on Statistics & Applied Probability, Taylor & Francis

  • Nelsen R (2006) An introduction to copulas. Springer Series in Statistics, Springer New York

  • Zhang K, Lin J, Huang C (2013) Some new results on weighted geometric mean for copulas. Int J Uncertain Fuzziness Knowl Based Syst 21(02):277–288

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

We are grateful to an associate editor and two anonymous reviewers for their valuable comments.

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Correspondence to Walter Diaz.

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Diaz, W., Cuadras, C.M. An extension of the Gumbel–Barnett family of copulas. Metrika 85, 913–926 (2022). https://doi.org/10.1007/s00184-022-00859-0

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  • DOI: https://doi.org/10.1007/s00184-022-00859-0

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