Document Type : Research Paper
Young Researchers and Elite Club, Maragheh branch, Islamic Azad University, Maragheh, Iran.
This study after reviewing construction methods of generators in Archimedean copulas (AC), proposes several useful lemmas related with generators of AC. Then a new trigonometric Archimedean family will be shown which is based on cotangent function. The generated new family is able to model the low dependence structures.
 T. Bacigal, R. Mesiar, and V. Najjari, Generators of copulas and aggregation, Information science, 306 (2015), pp. 81-87.
 T. Bacigal, V. Najjari, R. Mesiar, and Hasan Bal, Additive generators of copulas, Fuzzy Sets and Systems, 264 (2015), pp. 42-50.
 F. Durante, R. Foschi, and P. Sarkoci, Distorted copulas: constructions and tail dependence, Comm. Statist. Theory and Methods, 39 (2010), pp. 2288-2301.
 F. Durante and C. Sempi, Copula and semicopula transforms, Int. J. Math. Sci., (2005), pp. 645-655.
 V. Jagr, M. Komornikova, and R. Mesiar, Conditioning stable copulas, Neural Network World, 20 (2010), pp. 69-79.
 M. Junker and A. May, Measurement of aggregate risk with copulas, Econom. J., 8 (2005), pp. 428-454.
 E.P. Klement, R. Mesiar, and E. Pap, Triangular Norms, Kluwer Academic Publishers, Dordrecht, 2000.
 R. Mesiar, V. Jagr, M. Juranova, and M. Komornikova, Univariate Conditioning Of Copulas, Kybernetika, 44 (2008), pp. 807-816.
 F. Michiels and A. De Schepper, How to improve the fit of Archimedean copulasby means of transforms, Stat Papers, 53 (2012), pp. 345-355.
 F. Michiels and A. De Schepper, Understanding copula transforms: a review of dependence properties, Working Paper, 2009.
 F. Michiels, I. Koch, and A. De Schepper, A New Method for the Construction of Bivariate Archimedean Copulas Based on the $\lambda$ Function, Comm. Statist. Theory Methods, 40 (2011), pp. 2670-2679.
 V. Najjari and A. Rahimi, A note on ''generalized bivariate copulas and their properties'', Sahand Commun. Math. Anal., 2 (2015), pp. 61-64.
 R.B. Nelsen, An introduction to copulas, Second edition, Springer, New York, 2006.
 M. Pekarova, Construction of copulas with predetermined properties, PhD. Dissertation, 2012.
 B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North Holland, 1983.
 A. Sklar, Fonctions de repartitiona n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris. 8 (1959), pp. 229-231.