IDEAS home Printed from https://ideas.repec.org/a/inm/ordeca/v7y2010i2p196-214.html
   My bibliography  Save this article

Generalized Diagonal Band Copulas with Two-Sided Generating Densities

Author

Listed:
  • Samuel Kotz

    (Department of Engineering Management and Systems Engineering, The George Washington University, Washington, DC 20052)

  • Johan René van Dorp

    (Department of Engineering Management and Systems Engineering, The George Washington University, Washington, DC 20052)

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. Simulation 57 (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. Papers 36 (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 Methods 32 (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.

Suggested Citation

  • Samuel Kotz & Johan René van Dorp, 2010. "Generalized Diagonal Band Copulas with Two-Sided Generating Densities," Decision Analysis, INFORMS, vol. 7(2), pages 196-214, June.
    • Handle: RePEc:inm:ordeca:v:7:y:2010:i:2:p:196-214
    DOI: 10.1287/deca.1090.0162
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/deca.1090.0162
    Download Restriction: no
    File URL: https://libkey.io/10.1287/deca.1090.0162?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Ali E. Abbas, 2009. "Multiattribute Utility Copulas," Operations Research, INFORMS, vol. 57(6), pages 1367-1383, December.
    2. Ali E. Abbas & Ronald A. Howard, 2005. "Attribute Dominance Utility," Decision Analysis, INFORMS, vol. 2(4), pages 185-206, December.
    3. Woojune Yi & Vicki M. Bier, 1998. "An Application of Copulas to Accident Precursor Analysis," Management Science, INFORMS, vol. 44(12-Part-2), pages 257-270, December.
    4. Edward Frees & Ping Wang, 2005. "Credibility Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 9(2), pages 31-48.
    5. Lewandowski, Daniel, 2005. "Generalized diagonal band copulas," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 49-67, August.
    6. Robert T. Clemen & Terence Reilly, 1999. "Correlations and Copulas for Decision and Risk Analysis," Management Science, INFORMS, vol. 45(2), pages 208-224, February.
    7. Roger M. Cooke & Rudi Waij, 1986. "Monte Carlo Sampling for Generalized Knowledge Dependence with Application to Human Reliability," Risk Analysis, John Wiley & Sons, vol. 6(3), pages 335-343, September.
    8. Ali E. Abbas, 2006. "Maximum Entropy Utility," Operations Research, INFORMS, vol. 54(2), pages 277-290, April.
    9. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    10. Soofi, E. S. & Retzer, J. J., 2002. "Information indices: unification and applications," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 17-40, March.
    11. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    12. Paul Embrechts, 2009. "Copulas: A Personal View," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 639-650, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tianyang Wang & James S. Dyer, 2012. "A Copulas-Based Approach to Modeling Dependence in Decision Trees," Operations Research, INFORMS, vol. 60(1), pages 225-242, February.
    2. L. Robin Keller & Kelly M. Kophazi, 2012. "From the Editors ---Copulas, Group Preferences, Multilevel Defenders, Sharing Rewards, and Communicating Analytics," Decision Analysis, INFORMS, vol. 9(3), pages 213-218, September.
    3. Tim Bedford & Alireza Daneshkhah & Kevin J. Wilson, 2016. "Approximate Uncertainty Modeling in Risk Analysis with Vine Copulas," Risk Analysis, John Wiley & Sons, vol. 36(4), pages 792-815, April.
    4. L. Robin Keller & Kelly M. Kophazi, 2010. "From the Editors..," Decision Analysis, INFORMS, vol. 7(2), pages 151-154, June.
    5. Werner, Christoph & Bedford, Tim & Cooke, Roger M. & Hanea, Anca M. & Morales-Nápoles, Oswaldo, 2017. "Expert judgement for dependence in probabilistic modelling: A systematic literature review and future research directions," European Journal of Operational Research, Elsevier, vol. 258(3), pages 801-819.
    6. Andy Lewin & Ekundayo Shittu & Thomas Mazzuchi & Rene Dorp, 2021. "The correlation of cost and schedule variance in satellite programs: level of effort versus discrete cost accounts," Environment Systems and Decisions, Springer, vol. 41(2), pages 248-266, June.
    7. L. Robin Keller & Ali Abbas & J. Eric Bickel & Vicki M. Bier & David V. Budescu & John C. Butler & Enrico Diecidue & Robin L. Dillon-Merrill & Raimo P. Hämäläinen & Kenneth C. Lichtendahl & Jason R. W, 2012. "From the Editors ---Brainstorming, Multiplicative Utilities, Partial Information on Probabilities or Outcomes, and Regulatory Focus," Decision Analysis, INFORMS, vol. 9(4), pages 297-302, December.
    8. Donatella Vicari & Johan Ren� van Dorp, 2013. "On a bounded bimodal two-sided distribution fitted to the Old-Faithful geyser data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(9), pages 1965-1978, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ali E. Abbas, 2009. "Multiattribute Utility Copulas," Operations Research, INFORMS, vol. 57(6), pages 1367-1383, December.
    2. Smith, Michael Stanley, 2023. "Implicit Copulas: An Overview," Econometrics and Statistics, Elsevier, vol. 28(C), pages 81-104.
    3. Hernández-Bastida, A. & Fernández-Sánchez, M.P. & Gómez-Déniz, E., 2009. "The net Bayes premium with dependence between the risk profiles," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 247-254, October.
    4. Aldin Ardian & Mustafa Kumral, 2021. "Enhancing mine risk assessment through more accurate reproduction of correlations and interactions between uncertain variables," Mineral Economics, Springer;Raw Materials Group (RMG);Luleå University of Technology, vol. 34(3), pages 411-425, October.
    5. Michael Stanley Smith, 2021. "Implicit Copulas: An Overview," Papers 2109.04718, arXiv.org.
    6. Ozer-Imer, Itir & Ozkan, Ibrahim, 2014. "An empirical analysis of currency volatilities during the recent global financial crisis," Economic Modelling, Elsevier, vol. 43(C), pages 394-406.
    7. Benoumechiara Nazih & Bousquet Nicolas & Michel Bertrand & Saint-Pierre Philippe, 2020. "Detecting and modeling critical dependence structures between random inputs of computer models," Dependence Modeling, De Gruyter, vol. 8(1), pages 263-297, January.
    8. Ostap Okhrin & Martin Odening & Wei Xu, 2013. "Systemic Weather Risk and Crop Insurance: The Case of China," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(2), pages 351-372, June.
    9. MICHIELS, Frederik & DE SCHEPPER, Ann, 2007. "A copula test space model: How to avoid the wrong copula choice," Working Papers 2007027, University of Antwerp, Faculty of Business and Economics.
    10. Zhichao Zhang & Li Ding & Fan Zhang & Zhuang Zhang, 2015. "Optimal Currency Composition for China's Foreign Reserves: A Copula Approach," The World Economy, Wiley Blackwell, vol. 38(12), pages 1947-1965, December.
    11. repec:jss:jstsof:21:i04 is not listed on IDEAS
    12. Edward W. Frees & Gee Lee & Lu Yang, 2016. "Multivariate Frequency-Severity Regression Models in Insurance," Risks, MDPI, vol. 4(1), pages 1-36, February.
    13. Anderson, John D. & Harri, Ardian & Coble, Keith H., 2009. "Techniques for Multivariate Simulation from Mixed Marginal Distributions with Application to Whole-Farm Revenue Simulation," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 34(01), pages 1-15, April.
    14. Kwamie Dunbar & Albert J. Edwards, 2007. "Empirical Analysis of Credit Risk Regime Switching and Temporal Conditional Default Correlation in Credit Default Swap Valuation: The Market liquidity effect," Working papers 2007-10, University of Connecticut, Department of Economics.
    15. Ahmed Ghorbel & Wajdi Hamma & Anis Jarboui, 2017. "Dependence between oil and commodities markets using time-varying Archimedean copulas and effectiveness of hedging strategies," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(9), pages 1509-1542, July.
    16. Beccacece, Francesca & Borgonovo, Emanuele & Buzzard, Greg & Cillo, Alessandra & Zionts, Stanley, 2015. "Elicitation of multiattribute value functions through high dimensional model representations: Monotonicity and interactions," European Journal of Operational Research, Elsevier, vol. 246(2), pages 517-527.
    17. M. Reddy & Poulomi Ganguli, 2012. "Bivariate Flood Frequency Analysis of Upper Godavari River Flows Using Archimedean Copulas," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(14), pages 3995-4018, November.
    18. Robert T. Clemen & Gregory W. Fischer & Robert L. Winkler, 2000. "Assessing Dependence: Some Experimental Results," Management Science, INFORMS, vol. 46(8), pages 1100-1115, August.
    19. van Dorp, J. Rene, 2005. "Statistical dependence through common risk factors: With applications in uncertainty analysis," European Journal of Operational Research, Elsevier, vol. 161(1), pages 240-255, February.
    20. Werner, Christoph & Bedford, Tim & Cooke, Roger M. & Hanea, Anca M. & Morales-Nápoles, Oswaldo, 2017. "Expert judgement for dependence in probabilistic modelling: A systematic literature review and future research directions," European Journal of Operational Research, Elsevier, vol. 258(3), pages 801-819.
    21. Ali E. Abbas & Ronald A. Howard, 2005. "Attribute Dominance Utility," Decision Analysis, INFORMS, vol. 2(4), pages 185-206, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ordeca:v:7:y:2010:i:2:p:196-214. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.