Summary
We make some remarks on the problem how to construct probability measures with given marginals. Questions of this kind arise if one wants to build a stochastic model in a situation where one has some idea of the kind of dependence and knows exactly certain marginal distributions.
Similar content being viewed by others
References
Barnett, V. (1980). Some bivariate unfirom distributions,Comm. Statist. Theor. Meth., A,9, 453–461.
Bass, J. (1955). Sur la compatibilité des fonctions de répartition,C. R. Acad.,240, 839–841.
Bühler, W. J. and Mieschke, K. J. (1981). On (n−1)-wise and joint independence and normality ofn random variables: An example,Comm. Statist. Theor. Meth., A,10, 927–930.
Cook, R. D. and Johnson, M. E. (1981). A family of distributions for modelling nonelliptically symmetric multivariate data,J.R. Statist. Soc., B,43, 120–218.
Dall'Aglio, G. (1972). Fréchet classes and compatibility of distribution functions,Symp. Math.,9, 131–150.
Farlie, D. J. G. (1960). The performance of some correlation coefficients for a general bivariate distribution,Biometrika,47, 307–323.
Joffe, A. (1971). On a sequence of almost deterministic pair wise independent random variables,Proc. Amer. Math. Soc.,29, 381–382.
Joffe, A. (1974). On a set of almost deterministick-independent random variables,Ann. Prob.,2, 161–162.
Johnson, N. L. and Kotz, S. (1975). On some generalized Farlie-Gumbel-Morgenstern distributions,Commun. Statistics,4, 415–427.
Johnson, N. L. and Kotz, S. (1977). On some generalized Farlie-Gumbel-Morgenstern distributions—II. Regression, correlation and further generalizations,Comm. Statist. Theor. Meth., A,6, 485–496.
Kellerer, H. G. (1964a). Maßtheoretische Marginalprobleme,Math. Ann.,153, 168–198.
Kellerer, H. G. (1964b). Verteilungsfunktionen mit gegebenen Marginalverteilungen,Zeit. Wahrscheinlichkeitsth.,3, 247–270.
Kimeldorf, G. and Sampson, A. (1975a). One-parameter families of bivariate distributions with fixed marginals,Commun. Statistics,4, 293–301.
Kimeldorf, G. and Sampson, A. (1975b). Uniform representations of bivariate distributions,Comm. Statistics,4, 617–627.
Kotz, S. and Johnson, N. L. (1977). Propriétés de dépendence des distributions itérées généralisées à deux variables Farlie-Gumbel-Morgenstern,C.R. Acad. Paris,285, 277–280.
Lancaster, H. O. (1963). Correlation and complete dependence of random variables,Ann. Math. Statist.,34, 1315–1321.
Mardia, K. V. (1970a). A translation family of bivariate distributions and Fréchet's bounds,Sankhya, A,32, 119–122.
Mardia, K. V. (1970b).Families of Bivariate Distributions, Hafner, Darim.
Plackett, R. L. (1965). A class of bivariate distributions,J. Amer. Statist. Ass.,60, 516–522.
Schucany, W. R., Parr, W. C. and Boyer, J. E. (1978). Correlation structure in Farlie-Gumbel-Morgenstern distributions,Biometrika,65, 650–653.
Author information
Authors and Affiliations
About this article
Cite this article
Rüschendorf, L. Construction of multivariate distributions with given marginals. Ann Inst Stat Math 37, 225–233 (1985). https://doi.org/10.1007/BF02481093
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02481093