Abstract
In this paper, we advance new families of bivariate copulas constructed by distributional distortions of existing bivariate copulas. The distortions under consideration are based on the unit gamma distribution of two forms. When the initial copula is Archimedean, the induced copula is also Archimedean under the admissible parameter space. Properties such as Kendall’s tau coefficient, tail dependence coefficients and tail orders for the new families of copulas are derived. An empirical application to economic indicator data is presented.
Highlights
Copulas have been employed to study the extent of tail dependence in the context of risk management, finance and insurance
We introduce the UGII distortion and investigate Kendall’s tau coefficient, tail dependence coefficients and tail orders of the resulting family of copulas
The purpose of this paper has been to introduce new families of copulas based on distributional distortions
Summary
Copulas have been employed to study the extent of tail dependence in the context of risk management, finance and insurance. The upper tail or extremal dependence refers to the degree of dependence in the upper right tail behavior and is generally defined to be the conditional probability of a vector of multivariate random variables exceeding a large threshold given that a subset of the random vector already exceeds the threshold It is of interest in practice, for example, in modeling the dependence of large loss events among various assets or insurance policies. Let F (x, y) be the cumulative probability distribution (cdf) of a bivariate random vector (X, Y ), FX (x) and FY (y) be the respective marginal cdf’s of X and Y. Fischer and Köck (2010) present a general construction scheme of d-variate copulas, which generalizes the Archimedean family, study admissible conditions on the distortion functions and derive the tail dependence coefficients for power and dual power distortions.
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