Skip to main content Accessibility help

A Primer on Copulas for Count Data

  • Christian Genest (a1) and Johanna Nešlehová (a2)


The authors review various facts about copulas linking discrete distributions. They show how the possibility of ties that results from atoms in the probability distribution invalidates various familiar relations that lie at the root of copula theory in the continuous case. They highlight some of the dangers and limitations of an undiscriminating transposition of modeling and inference practices from the continuous setting into the discrete one.

    • Send article to Kindle

      To send this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      A Primer on Copulas for Count Data
      Available formats

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      A Primer on Copulas for Count Data
      Available formats

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      A Primer on Copulas for Count Data
      Available formats



Hide All
Avérous, J. and Dortet-Bernadet, J.-L. (2000) LTD and RTI dependence orderings. Canad. J. Statist., 28, 151157.
Cameron, A.C., Li, T., Trivedi, P.K. and Zimmer, D.M. (2004) Modeling the differences in counted outcomes using bivariate copula models: With application to mismeasured counts. Econom. J., 7, 566584.
Capéraà, P. and Genest, C. (1990) Concepts de dépendance et ordres stochastiques pour des lois bidimensionnelles. Canad. J. Statist., 18, 315326.
Carley, H. (2002) Maximum and minimum extensions of finite subcopulas. Comm. Statist. Theory Methods, 31, 21512166.
Choulakian, V. and De Tibeiro, J. (2000) Copules archimédiennes et tableaux de contingence à variables qualitatives ordinales. Rev. Statist. Appl., 48, 8396.
Conti, P.L. (1993) On some descriptive aspects of measures of monotone dependence. Metron, 51, 4360 (1994).
Denuit, M. and Lambert, P. (2005) Constraints on concordance measures in bivariate discrete data. J. Multivariate Anal., 93, 4057.
Embrechts, P., McNeil, A.J. and Straumann, D. (2002) Correlation and dependence in risk management: Properties and pitfalls. In Risk Management: Value at Risk and Beyond (Cambridge, 1998), pages 176223. Cambridge Univ. Press, Cambridge.
Esary, J.D. and Proschan, F. (1972) Relationships among some concepts of bivariate dependence. Ann. Math. Statist., 43, 651655.
Fang, Z. and Joe, H. (1992) Further developments on some dependence orderings for continuous bivariate distributions. Ann. Inst. Statist. Math., 44, 501517.
Frees, E.W. and Valdez, E.A. (1998) Understanding relationships using copulas. N. Amer. Act. J., 2, 125.
Genest, C. and Favre, A.-C. (2007) Everything you always wanted to know about copula modeling but were afraid to ask. J. Hydrologic Eng., 12, 347368.
Genest, C., Ghoudi, K. and Rivest, L.-P. (1995) A semiparametric estimation procedure of dependence parameters in multivariate families of distributions. Biometrika, 82, 543552.
Genest, C., Marceau, É. and Mesfioui, M. (2003) Compound Poisson approximations for individual models with dependent risks. Insurance Math. Econom., 32, 7391.
Genest, C. and Rémillard, B. (2004) Tests of independence and randomness based on the empirical copula process. Test, 13, 335370.
Genest, C., Rémillard, B. and Beaudoin, D. (2007) Omnibus goodness-of-fit tests for copulas: A review and a power study. Insurance Math. Econom., 42, in press.
Goodman, L.A. and Kruskal, W.H. (1954) Measures of association for cross classifications. J. Amer. Statist. Assoc., 49, 732764.
Hoeffding, W. (1940) Maßstabinvariante Korrelationstheorie für diskontinuierliche Verteilungen. Arch. Math. Wirt. Sozialforsch., 7, 470.
Joe, H. (1993) Multivariate dependence measures and data analysis. Comput. Statist. Data Anal., 16, 279297.
Joe, H. (1997) Multivariate Models and Dependence Concepts, volume 73 of Monographs on Statistics and Applied Probability. Chapman & Hall, London.
Joe, H. (2005) Asymptotic efficiency of the two-stage estimation method for copula-based models. J. Multivariate Anal., 94, 401419.
Kendall, M.G. (1945) The treatment of ties in ranking problems. Biometrika, 33, 239251.
Kim, G., Silvapulle, M.J. and Silvapulle, P. (2007) Comparison of semiparametric and parametric methods for estimating copulas. Comput. Statist. Data Anal., 51, 28362850.
Kimeldorf, G. and Sampson, A.R. (1987) Positive dependence orderings. Ann. Inst. Statist. Math., 39, 113128.
Kowalczyk, T. and Niewiadomska-Bugaj, M. (2001) An algorithm for maximizing Kendall’s τ. Comput. Statist. Data Anal., 37, 181193.
Lehmann, E.L. (1966) Some concepts of dependence. Ann. Math. Statist., 37, 11371153.
Marshall, A.W. (1996) Copulas, marginals, and joint distributions. In Distributions with Fixed Marginals and Related Topics (Seattle, WA, 1993), volume 28 of IMS Lecture Notes Monogr. Ser., pages 213222. Inst. Math. Statist., Hayward, CA.
McNeil, A.J., Frey, R. and Embrechts, P. (2005) Quantitative Risk Management: Concepts, Techniques, and Tools. Princeton University Press, Princeton, NJ.
Meester, S.G. and Mackay, R.J. (1994) A parametric model for cluster correlated categorical data. Biometrics, 50, 954963.
Mesfioui, M. and Tajar, A. (2005) On the properties of some nonparametric concordance measures in the discrete case. J. Nonparametr. Stat., 17, 541554.
Mikusinski, P., Sherwood, H. and Taylor, M.D. (1992) Shuffles of min. Stochastica, 13, 6174.
Nelsen, R.B. (1987) Discrete bivariate distributions with given marginals and correlation. Comm. Statist. B–Simulation Comput., 16, 199208.
Nelsen, R.B. (1999) An Introduction to Copulas, volume 139 of Lecture Notes in Statistics. Springer, New York.
Neslehova, J. (2004) Dependence of Non-Continuous Random Variables. Doctoral dissertation, Universität Oldenburg, Oldenburg, Germany.
Neslehova, J. (2007) On rank correlation measures for non-continuous random variables. J. Multivariate Anal., 98, 544567.
Oakes, D. (1982) A model for association in bivariate survival data. J. Roy. Statist. Soc. Ser. B, 44, 414422.
Pfeifer, D. and Neslehova, J. (2004) Modeling and generating dependent risk processes for IRM and DFA. Astin Bull., 34, 333360.
Scarsini, M. (1984) On measures of concordance. Stochastica, 8, 201218.
Schweizer, B. and Sklar, A. (1974) Operations on distribution functions not derivable from operations on random variables. Studia Math., 52, 4352.
Shih, J.H. and Louis, T.A. (1995) Inferences on the association parameter in copula models for bivariate survival data. Biometrics, 51, 13841399.
Sklar, A. (1959) Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris, 8, 229231.
Tchen, A.H. (1980) Inequalities for distributions with given marginals. Ann. Probab., 8, 814827.
Trégouët, D.-A., Ducimetière, P., Bocquet, V., Visvikis, S., Soubrier, F. and Tiret, L. (2004) A parametric copula model for analysis of familial binary data. Am. J. Hum. Genet., 64, 886893.
Vandenhende, F. and Lambert, P. (2003) Improved rank-based dependence measures for categorical data. Statist. Probab. Lett., 63, 157163.
Whitt, W. (1976) Bivariate distributions with given marginals. Ann. Statist., 4, 12801289.
Yaari, M.E. (1987) The dual theory of choice under risk. Econometrica, 55, 95115.
Yanagimoto, T. and Okamoto, M. (1969) Partial orderings of permutations and monotonicity of a rank correlation statistic. Ann. Inst. Statist. Math., 21, 489506.


Related content

Powered by UNSILO

A Primer on Copulas for Count Data

  • Christian Genest (a1) and Johanna Nešlehová (a2)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.