Document Type: Research Paper


Gazi University, Faculty of Science, Statistics Department, Ankara, Turkey.


There are several theorical results about order statistics and copulas in the literature that have  been mentioned also by Nelsen \cite{p20}. The present study after reviewing some of these results, relies on  simulation technique to investigate the mentioned results about order statistics and copulas. The study concentrates on two well known Archimedean Gumbel and Frank families in the case that marginal functions $F(k)$  and $G(k)$  have different distributions.


[1] M. Al-Harthy, S. Begg and R. Bratvold, Copulas: A new technique to model dependence in petroleum decision making, Journal of Petroleum Science and Engineering , 57 (2007) 195-208.

[2] S. Çelebioğlu, Archimedean copulas And An Application, Selcuk university journal of science, 22 (2003) 43-52.

[3] R. T. Clemen and T. Reilly, Correlations and Copulas for Decision and Risk Analysis, Management Science, 45 (1999) 208-224.

[4] N. I. Fisher, Copulas. In: Kotz, S., Read, C. B., Banks, D. L. (Eds.), Encyclopedia of Statistical Sciences, Wiley, New York. 1(1997) 159-163.

[5] A. Friend and E. Rogge, Correlation at First Sight, Economic Notes: Review of Banking, Finance and Monetary Economics, 2004.

[6] C. Genest and J. MacKay, Copules archimédienneset familles de loisbi dimensionnelles dont les margessontdonnés, Canad. J. Statistics, 14 (1986a) 145-159.

[7] C. Genest and J. MacKay, The joy of copula, Bivariate distributions with uniform marginals, Amer. Statistics, 40 (1986b) 280-285.

[8] L. Hua, and H. Joe, Tail order and intermediate tail dependence of multivariate copulas, Journal of Multivariate Analysis, 102 (2011) 1454-1471.

[9] V. Najjari, T. Bacigàl and H. Bal, An Archimedean copula family with hyperbolic cotangent generator, IJUFKS, Vol. 22 No. 5 (2014) 761-–768.

[10] V. Najjari and M. G. Ünsal, An Application of Archimedean Copulas for Meteorological Data, GU J Sci, 25(2) (2012) 301-306.

[11] R. B. Nelsen, An Introduction to copulas, Springer, New York, Second edition, 2006.

[12] J. A. Rodríguez-Lallena, and M. Ubeda-Flores, A new class of bivariate copulas, Statistics and Probability Letters, 66 (2004) 315-325.

[13] A. Sklar, Fonctions de répartition à n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris, 8 (1959) 229-231.