Name
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 (Bedford, T., A. M. H. Meeuwissen. 1997. Minimally informative distributions with given rank correlations for use in uncertainty analysis. J. Statist. Comput. Simulation57(1--4) 143--175) 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 (Ferguson, T. F. 1995. A class of symmetric bivariate uniform distributions. Statist. Papers36(1) 31--40) and Bojarski (Bojarski, J. 2001. A new class of band copulas---Distributions with uniform marginals. Technical report, Institute of Mathematics, Technical University of Zielona Góra, Zielona Góra, Poland). 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 (van Dorp, J. R., S. Kotz. 2003. Generalizations of two-sided power distributions and their convolution. Comm. Statist.: Theory and Methods32(9) 1703--1723) 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. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1287/deca.1090.0162 | Decision Analysis |
Keywords | DocType | Volume |
Two-Sided Generating Densities,GDB copula property,uniform marginals,copula,van Dorp,GDB copula,GDB copula generator function,expert judgement,GDB copula construction,value of information.,elicitation,random variable,probability assessment,GDB copula dependence parameter,Archimedean copula,Generalized Diagonal Band Copulas,probability distribution,Zielona G | Journal | 7 |
Issue | ISSN | Citations |
2 | 1545-8490 | 4 |
PageRank | References | Authors |
0.39 | 3 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| SAMUEL KOTZ | 1 | 94 | 24.41 |
| J. René van Dorp | 2 | 116 | 16.43 |
| van DorpJohan René | 3 | 4 | 0.39 |