A new bivariate extension of FGM copulas

Cécile Amblard (1) , Stéphane Girard (2)

1 TIMB
2 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems

We propose a new family of copulas generalizing the Farlie-Gumbel-Morgenstern (FGM) family and generated by two univariate functions. The main feature of this family is two permit the modeling of high positive dependence. In particular, it is established that the correlation range is [-3/4,1] and that the upper tail dependence coefficient can reach any value in [0,1]. Some examples of parametric subfamilies are provided.

Mots clés: Copulas; semiparametric family; measures of association; positive dependence.; positive dependence

Domaines: Probabilités [math.PR]; Statistiques [math.ST]; Théorie [stat.TH]

Cécile Amblard, Stéphane Girard. A new bivariate extension of FGM copulas. Metrika, 2009, 70 (1), pp.1-17. ⟨10.1007/s00184-008-0174-7⟩. ⟨inria-00134433v2⟩