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Existence of Multivariate Distributions with Given Marginals

In: Distributions With Given Marginals and Statistical Modelling

Author

Listed:
  • Ene-Margit Tiit

    (University of Tartu, Institute of Mathematical Statistics)

Abstract

Abstract Let P 1(k 1), P m (k m ) be given k j-variate discrete marginal distributions defined in the same probability space. The problem is to define a q-variate distribution having the distributions P j (k j ) as marginals. The task is easy to solve if q = k 1 + k 2 +⋯+ k m (i.e. all marginals are non-overlapping) and all given marginals are independent (orthogonal). In this case the common distribution is uniquely defined as the product of marginals. We consider the cases when 1. the given marginals have one or more common components and 2. the dependence structure between some components of different marginals is given. Necessary and sufficient conditions for existence of common distribution are given, an algorithm for construction is presented and several practical examples demonstrated.

Suggested Citation

  • Ene-Margit Tiit, 2002. "Existence of Multivariate Distributions with Given Marginals," Springer Books, in: Carles M. Cuadras & Josep Fortiana & José A. Rodriguez-Lallena (ed.), Distributions With Given Marginals and Statistical Modelling, pages 229-241, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-0061-0_24
    DOI: 10.1007/978-94-017-0061-0_24
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