Generalized diagonal band copulas with two-sided generating densities

Generalized diagonal band copulas with two-sided generating densities

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Article ID: iaor20104815
Volume: 7
Issue: 2
Start Page Number: 196
End Page Number: 214
Publication Date: Jun 2010
Journal: Decision Analysis
Authors: ,
Keywords: statistics: distributions
Abstract:

Copulas are joint continuous distributions with uniform marginals and have been proposed to capture probabilistic dependence between random variables. Maximum-entropy copulas introduced by Bedford and Meeuwissen (1997) provide the option of making minimally informative assumptions given a degree-of-dependence constraint between two random variables. Unfortunately, their distribution functions are not available in a closed form, and their application requires the use of numerical methods. In this paper, we study a subfamily of generalized diagonal band (GDB) copulas, separately introduced by Ferguson (1995) and Bojarski (2001). Similar to Archimedean copulas, GDB copula construction requires a generator function. Bojarski's GDB copula generator functions are symmetric probability density functions. In this paper, symmetric members of a two-sided framework of distributions introduced by van Dorp and Kotz (2003) shall be considered. This flexible setup allows for derivations of GDB copula properties resulting in novel convenient expressions. A straightforward elicitation procedure for the GDB copula dependence parameter is proposed. Closed-form expressions for specific examples in the subfamily of GDB copulas are presented, which enhance their transparency and facilitate their application. These examples closely approximate the entropy of maximum-entropy copulas. Application of GDB copulas is illustrated via a value-of-information decision analysis example.

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