c ⃝ Statistical Research and Training Center J. Statist. Res. Iran 9 (2012): 147–158 ١۵٨–١۴٧ ، ﺻﺺ١٣٩١ ، ﭘﺎﯾﯿﺰ و زﻣﺴﺘﺎن٢ ، ﺷﻤﺎرهی٩ دورهی Some Results on a Generalized Archimedean Family of Copulas Ali Dolati ∗ and Mojdeh Karbasian Yazd University Abstract. Durante et al. (2007) introduced a class of bivariate copulas depending on two generators which generalizes some known families such as the Archimedean copulas. In this paper we provide some result on properties of this family when the generators are certain univariate survival functions. Keywords. Copula; Archimedean copula; dependence ordering; survival function. MSC 2010: 62H20, 60E15. 1 Introduction The construction of distributions with given marginals has been a subject to various lines of statistical research. In view of Sklar’s Theorem (Sklar, 1959) this problem can be reduced to the construction of a copula. Nelsen (2006) summarizes different methods of constructing copulas. Among these meth- ods, constructing principles for copulas based on certain univariate functions have gained in importance: see, for instance Amblard and Girard (2002), Rodr ´ iguez–Lallena and ´ Ubeda–Flores (2004), Morillas (2005), Fischer and Klein (2006), Durante (2007) and Durante et al. (2007). Most frequently, Archimedean copulas are used which constructed by composition of a spe- cific generator and its pseudo inverse: see, for instance Genest and Rivest (1993) and Av´ erous and Dortet–Bernadet (2004). Durante, et al. (2007) introduced a class of bivariate copulas, depending on two generators which * Corresponding author