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Constructing Multivariate Distributions with Specific Marginal Distributions

Author

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  • Koehler, K. J.
  • Symanowski, J. T.

Abstract

A method is presented for constructing multivariate distributions with any specific set of univariate marginal distributions. This construction provides a rich class of distributions for modeling multivariate data as well as a basis for easily simulating correlated observations. The joint cdf and joint density function are expressed as explicit functions of the cdf's and density functions for the univariate marginal distributions. The inclusion of different association parameters for different subsets of variables allows for many different patterns of associations. General properties of this class of multivariate distributions are reviewed and contour plots of selected bivariate densities are presented to illustrate the variety of possible shapes. An application to multivariate survival analysis is briefly considered.

Suggested Citation

  • Koehler, K. J. & Symanowski, J. T., 1995. "Constructing Multivariate Distributions with Specific Marginal Distributions," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 261-282, November.
    • Handle: RePEc:eee:jmvana:v:55:y:1995:i:2:p:261-282
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    Cited by:

    1. Dominique Guegan & Bertrand Hassani, 2014. "Stress Testing Engineering: the real risk measurement?," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00951593, HAL.
    2. Paola Palmitesta & Corrado Provasi, 2005. "Aggregation of Dependent Risks Using the Koehler–Symanowski Copula Function," Computational Economics, Springer;Society for Computational Economics, vol. 25(1), pages 189-205, February.
    3. Matthias Fischer & Christian Köck, 2007. "Multivariate Copula Models at Work: Dependence Structure of Energie Prices," Energy and Environmental Modeling 2007 24000014, EcoMod.
    4. Han-Ying Liang & Jacobo Uña-Álvarez, 2011. "Asymptotic properties of conditional quantile estimator for censored dependent observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(2), pages 267-289, April.
    5. Fischer, Matthias J. & Köck, Christian & Schlüter, Stephan & Weigert, Florian, 2007. "Multivariate Copula Models at Work: Outperforming the desert island copula?," Discussion Papers 79/2007, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    6. Liang, Han-Ying & Peng, Liang, 2010. "Asymptotic normality and Berry-Esseen results for conditional density estimator with censored and dependent data," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1043-1054, May.
    7. George-Williams, H. & Wade, N. & Carpenter, R.N., 2022. "A probabilistic framework for the techno-economic assessment of smart energy hubs for electric vehicle charging," Renewable and Sustainable Energy Reviews, Elsevier, vol. 162(C).
    8. Cai, Zongwu, 2001. "Estimating a Distribution Function for Censored Time Series Data," Journal of Multivariate Analysis, Elsevier, vol. 78(2), pages 299-318, August.
    9. Liang, Han-Ying & de Ua-lvarez, Jacobo, 2009. "A Berry-Esseen type bound in kernel density estimation for strong mixing censored samples," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1219-1231, July.
    10. Paola Palmitesta & Corrado Provasi, 2004. "Aggregation of Dependent Risks with Specific Marginals by the Family of Koehler-Symanowski Distributions," Computing in Economics and Finance 2004 306, Society for Computational Economics.
    11. Zhou, Xing-cai & Xu, Ying-zhi & Lin, Jin-guan, 2017. "Wavelet estimation in varying coefficient models for censored dependent data," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 179-189.
    12. Liebscher, Eckhard, 2008. "Construction of asymmetric multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2234-2250, November.
    13. Dominique Guegan & Bertrand Hassani, 2014. "Stress Testing Engineering: the real risk measurement?," Post-Print halshs-00951593, HAL.

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