Document Type: Research Paper

Authors

1 Young Researchers and Elite Club, Maragheh branch, Islamic Azad University, Maragheh, Iran.

2 Department of Mathematics, University of Maragheh, P.O.Box 55181- 83111, Maragheh, Iran.

Abstract

In 2004, Rodr'{i}guez-Lallena and '{U}beda-Flores have introduced a class of bivariate copulas which generalizes some known families such as the Farlie-Gumbel-Morgenstern distributions. In 2006, Dolati and '{U}beda-Flores presented multivariate generalizations of this class. Then in 2011, Kim et al. generalized Rodr'{i}guez-Lallena and '{U}beda-Flores' study to any given copula family. But there are some inaccuracies in the study by Kim et al. We mean to consider the interval for the parameter proposed by Kim et al. and show that it is inaccurate.

Keywords

[1] T. Bacig'{a}l, R. Mesiar, V. Najjari, Generators of copulas and aggregation, Information Sciences,  306 (2015) 81--87.

[2] T. Bacig'{a}l, V. Najjari, R. Mesiar, H. Bal, Additive generators of copulas, Fuzzy Sets and Systems, 264 (2015) 42--50.

[3] H. Bal, V. Najjari, Archimedean copulas family via hyperbolic generator, Gazi University Journal of Science, 26(2): (2013) 195--200.

[4] H. Bekrizadeh, G. A. Parham. M. R. Zadkarmi,  The New Generalization of Farlie–Gumbel–Morgenstern Copulas, Applied Mathematical Sciences,  6(71) (2012) 3527--3533.

[5] H. Bekrizadeh, G. A. Parham. M. R. Zadkarmi,  A new class of positive dependent bivariate copula and its properties, Proc. of the 2nd Workshop on Copula and its Applications,  (2012) 12--21.

[6] A. Dolati, M. '{U}beda-Flores,  Some new parametric families of multivarite copulas, International Mathematical Forum,  1 (2006) 17--25.

[7] J. M. Kim, E. A. Sungur, T. Choi, T. Y. Heo, Generalized bivariate copulas and their properties, Model Assisted Statistics and Applications, 6 (2011) 127--136.

[8] R. Mesiar, J. Komorn'{i}k, M. Komorn'{i}kov'{a}, On some construction methods for bivariate copulas, Advances in Intelligent Systems and Computing, 228 (2013)  39--45.

[9] R. Mesiar, V. Najjari, New families of symmetric/asymmetric copulas, Fuzzy Sets and Systems, 252 (2014) 99--110.

[10] V. Najjari., T. Bacig'{a}l., H. Bal.,  An Archimedean Copula Family with Hyperbolic Cotangent Generator, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 22(5): (2014) 761--768.

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

[12] J. A. Rodr'{i}guez-Lallena, M.  '{U}beda-Flores, A new class of bivariate copulas, Statistics and Probability Letters, 66 (2004) 315-325.

[13] S. T. c{S}ahin Tekin, V. Najjari, H. H. "{O}rkc"{u}, Simulation study on copulas, Sahand Communications in Mathematical Analysis, 1(2) (2014) 55--63.