Arşimedyen kapulalar ve bir uygulama

Arşimedyen kapulalar özellikle son yıllarda uygulamalarda sıklıkla kullanılmaya başlamıştır. Bu çalışmada bu kapulaların temel özellikleri, iki parametreli ve ikiden çok değişkenli aileleri ile birlikte bu alanda ortaya çıkan yeni gelişmelere değinilmiştir. Ayrıca iki örnek uygulamaya yer verilmiştir.

Archimedean copulas and an application

Especially in the last years, the Archimedean copulas take place more frequently in the applications. In this study, it is tried to introduce the Archimedean copulas with their basic properties, two parameter families and the multivariate families meanwhile some new developments are touched on. In addition, two applications for the student examination scores are given.

___

1. Schweizer, B., Sklar, A., Probabilistic Metric Spaces, North Holland, New York (1983).

2. Nelsen,R.B., An Introduction to Copulas, Springer, New York (1999).

3. Juri, A., Wüthrich,M.V., Copula convergence theorems for tail events, Insurance Math. Econ., 30(3), 405-420 (2002).

4. Hennessy, D.A., Lapan, D.E., The use of Archimedean copulas to model portfolio allocations, Math Finance, 12(2), 143-155 (2002).

5. Gray, R.J.,Li, Y., Optimal weight functions for marginal proportional hazards analysis of clustered failure time data, Lifetime Dat Anal, 8(1), 5-19 (2002).

6. Wang, W.J., Wells, M.T., Model selection and semiparametric inference for bivariate failure-time data, J. Amer. Statist. Assoc., 95(449), 62-72 (2000).

7. Genest, C., MacKay, J., Copules archimédiennes et familles de lois bidimensionelles dont les marges sont données, Canad. J. Statist., 14, 145-159 (1986).

8. Genest, C., MacKay, J., The joy of copulas: bivariate distributions with uniform marginals, Amer. Statist., 40, 280-285 (1986).

9. Nelsen, R.B., Dependence and order in Archimedean copulas, J. Multivariate Anal., 60(1), 111-122 (1997).

10. Joe, H., Multivariate Models and Dependence Concepts, Chapman and Hall, London (1997).

11. Lu, J.C., Bhattacharyya, G.K., Some new constructions of bivariate Weibull models, Ann. Inst. Stat. Math., 42, 543- 559 (1990).

12. Joe, H., Parametric families of multivariate distributions with given margins, J. Multivariate Anal., 46, 262-282 (1993).

13. Çelebioğlu, S., Archimedean copulas generated by the analytical means of generators, Araştırma Sempozyumu ’97, Ankara 24-26 Kasım 1997, Araştırma Sempozyumu ’97 Bildirileri, 32-36,Ankara (1997).

14. Çelebioğlu, S., On a one-parametric family of copulas, İstatistik Günleri Sempozyumu, Adana 25-26 Mayıs 1998, İstatistik Günleri Sempozyumu Bildiriler Kitabı, 1-4, Ankara (1998).

15. Çelebioğlu, S., Toplamsal Arşimedyen üreticilerden türetilen yeni bir kapulalar ailesi, İstatistik Konferansı, Ankara 26-27 Ekim 1998, İstatistik Konferansı Bildiriler Kitabı, 31-35, Ankara (1999).

16. Capéraà, P., Fougères, A.-L., Genest, C., Bivariate distributions with given extreme value attractor, J. Multivariate Anal., 72, 30-49 (2000).

17. Joe, H., Ma, C., Multivariate survival functions with a min-stable property, J. Multivariate Anal., 75, 13-35 (2000).

18. Sungur, E.A., Some results on truncation dependence invariant class of copulas, Commun. Statist. Theory-Meth., 31(8), 1399-1422 (2002).

19. Genest, C., Ghoudi, K., Rivest, L.-P., Comment on the paper by E.W. Frees and E.A. Valdez (1998), North American Actuarial Journal, 2, 143-149 (1998).

20. Cuculescu, I., Theodorescu, R., Extreme value attractors for star unimodal copulas, C.R. Acad. Sci. Paris Sér. I Math., 334, 689-692 (2002).

21. Genest, C., Marceau, E., Mesfioui, M., Compound Poisson approximations for individual models with dependent risks, Insurance Math. Econ., 32(1), 73-91, FEB 19 (2003).

22. Genest, C., Rivest, L.-P., Statistical inference procedures for bivariate Archimedean copulas, J. Amer. Statist. Assoc., 88, 1034-1043 (1993).

23. Sungur, E.A., Yang, Y., Diagonal copulas of Archimedean class, Commun. Statist. Theory-Meth., 25(7), 1659-1676 (1996).