Existence of Multivariate Distributions with Given Marginals

Ene-Margit Tiit
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Ene-Margit Tiit: University of Tartu, Institute of Mathematical Statistics

A chapter in Distributions With Given Marginals and Statistical Modelling, 2002, pp 229-241 from Springer

Abstract: 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.

Keywords: Characterization of joint distributions; regular class of index sets (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-0061-0_24

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DOI: 10.1007/978-94-017-0061-0_24

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