Further Results for a General Family of Bivariate Copulas

Izadkhah, S.; Ahmadzade, Hamed; Amini, Mohammad

doi:10.1080/03610926.2013.824100

Cited by 1 publication

(2 citation statements)

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“…with a generator h(x) = x/(1 − |θ|(1 − x)) in our case. Furthermore, Example 3.2 in [24] refers to C θ , 0 ≤ θ ≤ 1, as a generalized Ali-Mikhail-Haq copula. Making use now of Theorem 2.1 of the same reference [23], we establish that C θ is a copula if and only if |θ| ≤ 1.…”

Section: Upper Bound Copulamentioning

confidence: 99%

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On the Ratio-Type Family of Copulas

El Ktaibi,

Bentoumi,

Mesfioui

2024

Mathematics

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Investigating dependence structures across various fields holds paramount importance. Consequently, the creation of new copula families plays a crucial role in developing more flexible stochastic models that address the limitations of traditional and sometimes impractical assumptions. The present article derives some reasonable conditions for validating a copula of the ratio-type form uv/(1−θf(u)g(v)). It includes numerous examples and discusses the admissible range of parameter θ, showcasing the diversity of copulas generated through this framework, such as Archimedean, non-Archimedean, positive dependent, and negative dependent copulas. The exploration extends to the upper bound of a general family of copulas, uv/(1−θϕ(u,v)), and important properties of the copula are discussed, including singularity, measures of association, tail dependence, and monotonicity. Furthermore, an extensive simulation study is presented, comparing the performance of three different estimators based on maximum likelihood, ρ−inversion, and the moment copula method.

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Section: Upper Bound Copulamentioning

confidence: 99%

“…To explore the extent of positive dependence characterized by the proposed copula, we provide an overview of the commonly employed measures of association for bivariate copulas (see [24]). Proposition 3.9.…”

Section: Measures Of Associationmentioning

confidence: 99%