Bivariate Continuous Distributions

  • Thomas W. Yee
Chapter
Part of the Springer Series in Statistics book series (SSS)

Abstract

This chapter lists a small number of bivariate distributions whose parameters can easily be estimated by IRLS. A handful of a special type of bivariate distribution, called copulas, are also implemented. Some special consideration is given to the bivariate normal distribution and Plackett’s bivariate distribution.

Keywords

Marginal Distribution Multivariate Normal Distribution Multivariate Distribution Bivariate Distribution Bivariate Normal Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

References

  1. Balakrishnan, N. and C.-D. Lai 2009. Continuous Bivariate Distributions (Second ed.). New York: Springer.MATHGoogle Scholar
  2. Joe, H. 2014. Dependence Modeling with Copulas. Boca Raton, FL, USA: Chapman & Hall/CRC.Google Scholar
  3. Johnson, N. L., S. Kotz, and N. Balakrishnan 1997. Discrete Multivariate Distributions. New York, USA: John Wiley & Sons.MATHGoogle Scholar
  4. Kocherlakota, S. and K. Kocherlakota 1992. Bivariate Discrete Distributions. New York, USA: Marcel Dekker.MATHGoogle Scholar
  5. Mai, J.-F. and M. Scherer 2012. Simulating Copulas: Stochastic Models, Sampling Algorithms, and Applications. London: Imperial College Press.CrossRefGoogle Scholar
  6. Marshall, A. W. and I. Olkin 2007. Life Distributions: Structure of Nonparametric, Semiparametric, and Parametric Families. New York, USA: Springer.Google Scholar
  7. Mikosch, T. 2006. Copulas: tales and facts (with rejoinder). Extremes 9(1): 3–20,55–62.Google Scholar
  8. Nelsen, R. B. 2006. An Introduction to Copulas (Second ed.). New York, USA: Springer.MATHGoogle Scholar
  9. Plackett, R. L. 1965. A class of bivariate distributions. Journal of the American Statistical Association 60(310):516–522.MathSciNetCrossRefGoogle Scholar
  10. Schepsmeier, U. and J. Stöber 2014. Derivatives and Fisher information of bivariate copulas. Statistical Papers 55(2):525–542.MATHMathSciNetCrossRefGoogle Scholar
  11. Sklar, A. 1959. Fonctions de répartition à n dimensions et leurs marges. Publications de l’Institut de Statistique de L’Université de Paris 8:229–231.MathSciNetGoogle Scholar
  12. Trivedi, P. K. and D. M. Zimmer 2005. Copula modeling: An introduction for practitioners. Foundations and Trends in Econometrics 1(1):1–111.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Thomas Yee 2015

Authors and Affiliations

  • Thomas W. Yee
    • 1
  1. 1.Department of StatisticsUniversity of AucklandAucklandNew Zealand

Personalised recommendations