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The paper introduces a method for the construction of bivariate copulas with the usage of specific values of the parameters α and β (α,β transformation) and the parameters κ and λ in their domain. The produced bivariate copulas are defined in four subrectangles of the unit square. The bounds of the produced copulas are investigated, while a novel c...
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A new family of multivariate copulas constructed from existing copulas by transforming the corresponding random variables using their conditional distributions are introduced. It is shown that for symmetrical copulas in a triangular scheme, this transformation tends to asymptotic independence.
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Citations
... By appealing to (31), the c.d.f. of (T, X) in (32) is rewritten as ...
... In general, the literature on copula theory partly includes the methods of construction of new copulas of two dependent random variables (cf. Balakrishnan and Lai [27], Mesiar et al. [28], Durante et al. [29], Bedford and Wilson [30], Giakoumakis and Papadopoulos [31], and Alshehri and Kayid [32]). In turn, this paper also plays its role in the study of the generation of new copulas in the context of degradation models. ...
There are a variety of degradation models in the literature, each with a certain effect of random variation around the mean degradation path on the time-to-failure of the device being degraded. To assess the dependence that the random variation around the mean degradation path exerts on the resulting time-to-failure, this paper presents copula functions for time-to-failure-based degradation models with respect to two well-known degradation models, namely, the multiplicative degradation model and the additive degradation model. The implied copula functions for the case of the multiplicative degradation model have explicit forms. The implied copula functions are proved to be symmetric in the case of deterministic effect of degradation on failure, but the copulas obtained when failure is affected uncertainly by degradation are asymmetric. Necessary and sufficient conditions for the implicit copula functions to be symmetric are given.
