BazEkon - Biblioteka Główna Uniwersytetu Ekonomicznego w Krakowie

BazEkon home page

Meny główne

Autor
Chesneau Christophe (University of Caen-Normandie, France)
Tytuł
Diverse Copulas through Durante's Method. Exploring Parametric Functions
Źródło
Operations Research and Decisions, 2024, vol. 34, no. 3, s. 61-86, rys., tab., bibliogr. 28 poz.
Słowa kluczowe
Badania operacyjne, Modele matematyczne, Modelowanie matematyczne, Prognozowanie matematyczne
Operations research, Mathematical models, Mathematical modeling, Mathematical forecasting
Uwagi
summ.
Abstrakt
This article unveils the often underestimated potential of a copula methodology introduced by Durante in 2009. It highlights the remarkable ability of the method to generate a broad spectrum of copulas by exploiting various parametric functions. Our exploration encompasses a collection of power-like, exponential-like, trigonometric-like, logarithmic-like, hyperbolic-like and error-like functions, each dependent on one, two, or three parameters, effectively satisfying the necessary assumptions of Durante's method. The proofs provided rely on suitable differentiation, comprehensive factorizations, and judicious application of mathematical inequalities. In the vast repertoire of copulas derived from this methodology, we present three distinct series of eight new copulas, supported by a graphical analysis of their respective densities. This theoretical study not only expands the understanding of copula generation but also introduces a new perspective on their construction in various contexts. (original abstract)
Dostępne w
Biblioteka Główna Uniwersytetu Ekonomicznego w Krakowie
Pełny tekst
Pokaż
Bibliografia
Pokaż
  1. Ali, M. M., Mikhail, N. N., and Haq, M. S. A class of bivariate distributions including the bivariate logistic. Journal of Multivariate Analysis 8, 3 (1978), 405-412.
  2. Barnett, V. Some bivariate uniform distributions. Communications in Statistics - Theory and Methods 9, 4 (1980), 453-461.
  3. Celebioğlu, S. A way of generating comprehensive copulas. Gazi University Journal of Institute of Science and Technology 10, 1 (1997), 57-61.
  4. Chesneau, C. On new types of multivariate trigonometric copulas. AppliedMath 1, 1 (2021), 3-17.
  5. Chesneau, C. On the Gumbel-Barnett extended Celebioglu-Cuadras copula. Japanese Journal of Statistics and Data Science 6, 2 (2023), 759-781.
  6. Chesneau, C. A revisit of the modified Celebioglu-Cuadras copula. Electronic Journal of Mathematical Analysis and Applications 11, 2 (2023), 10.
  7. Clayton, D. G. A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65, 1 (1978), 141-151.
  8. Cuadras, C. M. Constructing copula functions with weighted geometric means. Journal of Statistical Planning and Inference 139, 11 (2009), 3766-3772.
  9. Dolati, A., Mohseni, S., and Úbeda Flores, M. Some results on a transformation of copulas and quasi-copulas. Information Sciences 257 (2014), 176-182.
  10. Durante, F. Construction of non-exchangeable bivariate distribution functions. Statistical Papers 50, 2 (2009), 383-391.
  11. Durante, F., and Sempi, C. Principles of Copula Theory. Taylor & Francis, New York, 2015.
  12. El Ktaibi, F., Bentoumi, R., Sottocornola, N., and Mesfioui, M. Bivariate copulas based on counter-monotonic shock method. Risks 10, 11 (2022), 202.
  13. Eyraud, H. The principles of correlation measurement. Annales de l'Université de Lyon. Sciences. Section A, Sciences Mathématiques et Astronomie 1, 30-47 (1936), 111 (in French).
  14. Frank, M. J. On the simultaneous associativity of F(x, y) and x + y - F(x, y). Aequationes mathematicae 19 (1979), 194-226.
  15. Gumbel, E. J. Bivariate exponential distributions. Journal of the American Statistical Association 55, 292 (1960), 698-707.
  16. Gumbel, E. J. Bivariate logistic distributions. Journal of the American Statistical Association 56, 294 (1961), 335-349.
  17. Hougaard, P. A class of multivariate failure time distributions. Biometrika 73, 3 (1986), 671-678.
  18. Joe, H. Multivariate Models and Multivariate Dependence Concepts. Vol. 73 of Monographs on Statistics & Applied Probability. Chapman & Hall/CRC, London, 1997.
  19. Michimae, H., and Emura, T. Likelihood inference for copula models based on left-truncated and competing risks data from field studies. Mathematics 10, 13 (2022), 2163.
  20. Mukherjee, S., Lee, Y., Kim, J.-M., Jang, J., and Park, J.-S. Construction of bivariate asymmetric copulas. Communications for Statistical Applications and Methods 25, 2 (2018), 217-234.
  21. Nelsen, R. B. An Introduction to Copulas. Springer Series in Statistics. Springer, New York, 2007.
  22. Poonia, P. K., and Singh, V. V. Stochastic analysis of delayed reporting of faults in a computer network using copula distribution. International Journal of Quality Engineering and Technology 9, 2 (2023), 161-182.
  23. Shih, J.-H., Konno, Y., Chang, Y.-T., and Emura, T. Copula-based estimation methods for a common mean vector for bivariate meta-analyses. Symmetry 14, 2 (2022), 186.
  24. Strauch, O., and Baláž, V. Copulas. Uniform distribution theory 18, 1 (2023), 47-200.
  25. Susam, S. O. Parameter estimation of some Archimedean copulas based on minimum Cramér-von-Mises distance. Journal of the Iranian Statistical Society 19, 1 (2019), 163-183.
  26. Susam, S. O. A new family of Archimedean copula via trigonometric generator function. Gazi University Journal of Science 33, 3 (2020), 806-813.
  27. Vaughan, H. E. The expression 00. The Mathematics Teacher 63 (1970), 111-112.
  28. Yeh, C.-T., Liao, G.-Y., and Emura, T. Sensitivity analysis for survival prognostic prediction with gene selection: A copula method for dependent censoring. Biomedicines 11, 3 (2023), 797.
Cytowane przez
Pokaż
ISSN
2081-8858
2391-6060
Język
eng
URI / DOI
http://dx.doi.org/10.37190/ord240304
Udostępnij na Facebooku Udostępnij na Twitterze Udostępnij na Google+ Udostępnij na Pinterest Udostępnij na LinkedIn Wyślij znajomemu