Generalized Diagonal Band Copulas with Two-Sided Generating Densities

Authors:
Samuel Kotz;Johan René van Dorp
Affiliations:
Department of Engineering Management and Systems Engineering, The George Washington University, Washington, DC 20052;Department of Engineering Management and Systems Engineering, The George Washington University, Washington, DC 20052
Venue:
Decision Analysis
Year:
2010

Citing 8
Cited 4

An application of copulas to accident precursor analysis

Management Science
Correlations and Copulas for Decision and Risk Analysis

Management Science
Making Hard Decisions with Decisiontools Suite

Making Hard Decisions with Decisiontools Suite
An Introduction to Copulas (Springer Series in Statistics)

An Introduction to Copulas (Springer Series in Statistics)
Maximum Entropy Utility

Operations Research
Attribute Dominance Utility

Decision Analysis
Measuring the coupled risks: A copula-based CVaR model

Journal of Computational and Applied Mathematics
Multiattribute Utility Copulas

Operations Research

From the Editors...

Decision Analysis
A Copulas-Based Approach to Modeling Dependence in Decision Trees

Operations Research
From the Editors---Copulas, Group Preferences, Multilevel Defenders, Sharing Rewards, and Communicating Analytics

Decision Analysis
From the Editors---Brainstorming, Multiplicative Utilities, Partial Information on Probabilities or Outcomes, and Regulatory Focus

Decision Analysis

Quantified Score

Hi-index	0.00

Visualization

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.