Bounds for the Clayton copula

Abstract

We provide two upper bounds on the Clayton copula Cθ(u1,...,un) if θ > 0 and n ≥ 2 and a lower bound in the case θ ∈ [-1,0) and n ≥ 2. The obtained bounds provide a nice probabilistic interpretation related to some negative dependence structures and also allow defining three new two-dimensional copulas which tighten the classical Fréchet–Hoeffding bounds for the Clayton copula when n = 2.

Ruin probability for the bi-seasonal discrete time risk model with dependent claims

“…Clayton copula can be used to model negative dependence when θ ∈ [−1, 0). Detailed analysis of this copula can be found, for instance, in [18,20,21] and [22]. In this example, the marginal distribution of X is Poisson with parameter 0.3, and the marginal distribution of Y is Poisson with parameter 1.4.…”

“…Clayton copula can be used to model negative dependence when θ ∈ [−1, 0). Detailed analysis of this copula can be found, for instance, in [18,20,21] and [22].…”

Correlation analysis of diabetes based on Copula

“…In Section 2, we discussed that the Clayton Copula is particularly sensitive to changes in the lower tail of variable distribution, and can more accurately reflect changes in the lower tail between variables ( 22 ). In our study, the lower tail portion of the variables is evident by an increase in TG/HDL-C accompanied by an increase in Glu or HbA1C.…”

A copula-based bivariate integer-valued autoregressive process with application

“…The Clayton copula can also account for negative dependence when θ ∈ [−1, 0). For more properties of this copula, see the recent paper by Manstavičius and Leipus [14].…”

“…Assume now that the Poisson innovations R 1,t and R 2,t with parameters λ 1 and λ 2 , respectively, are linked by a copula with the dependence parameter θ. Taking into account equality (14), we can estimate θ by minimizing the sum of squared differences…”