We propose a more flexible symmetric counterpart of the Huang–Kotz’s copula of the 1st type. Both the counterpart and Huang–Kotz’s copula of the 1st type provide the same improvement in the correlation level. Moreover, the proposed copula includes special cases of many other extensions of the Farlie–Gumbel–Morgenstern (FGM) copula.

We propose a more flexible symmetric counterpart of the Huang-Kotz's copula of the 1st type. Both the counterpart and Huang-Kotz's copula of the 1st type provide the same improvement of the correlation level. Moreover, the proposed copula includes special cases of many other extensions of the Farlie-Gumbel-Morgenstern (FGM) copula.