Constructing Generalized FGM Copulas by Means of Certain Univariate Distributions

Risk concentration based on Expectiles for extreme risks under FGM copula

“…This model has been generalized in various ways, for example, from two dimensions to higher dimensions or with more general form of (1 − u)(1 − v) in (2.5); see Cambanis (1977), Sarmanov (1966, Fischer and Klein (2007), among others. Here we focus on two generalizations.…”

On a general structure of the bivariate FGM type distributions

“…For the special case W (u, 1) = W (1, u) = 0, for all u ∈ I, the marginal distribution functions of (2.1) are F 1 and F 2 . Distributions of this form are well studied in [11], [15], [20]. R e m a r k 2.…”

“…have been introduced in the literature, e.g., [2], [4], [5], [3], [6], [9], [11], [14], [15], [16], [17], [20]. Lai and Xie [16] considered a representation of the FGM bivariate distribution possessing positive quadrant dependence property of the form (1.2) H(x, y) = F 1 (x)F 2 (y) + W (x, y) for all x, y, with nonnegative W (x, y) satisfying certain regularity conditions ensuring that H(x, y) is a bivariate distribution function.…”

Copula Theory: An Introduction

“…A complete survey about these generalized EFGM models of dependence is given in [40], where a list of several other references can be also found. More recent investigations are also provided in [4,5,6,65,169]. Another possible approach for extending EFGM copulas is based on the construction of copulas that are quadratic in one variable [163,170].…”