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Binary distributions of concentric rings

Author

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  • Wermuth, Nanny
  • Marchetti, Giovanni M.
  • Zwiernik, Piotr

Abstract

We introduce families of jointly symmetric, binary distributions that are generated over directed star graphs whose nodes represent variables and whose edges indicate positive dependences. The families are parametrized in terms of a single parameter. It is an outstanding feature of these distributions that joint probabilities relate to evenly spaced concentric rings. Kronecker product characterizations make them computationally attractive for a large number of variables. We study the behavior of different measures of dependence and derive maximum likelihood estimates when all nodes are observed and when the inner node is hidden.

Suggested Citation

  • Wermuth, Nanny & Marchetti, Giovanni M. & Zwiernik, Piotr, 2014. "Binary distributions of concentric rings," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 252-260.
    • Handle: RePEc:eee:jmvana:v:130:y:2014:i:c:p:252-260
    DOI: 10.1016/j.jmva.2014.05.010
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    References listed on IDEAS

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    1. Linzer, Drew A. & Lewis, Jeffrey B., 2011. "poLCA: An R Package for Polytomous Variable Latent Class Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 42(i10).
    2. Teugels, Jozef L, 1990. "Some representations of the multivariate Bernoulli and binomial distributions," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 256-268, February.
    3. Friedrich Schmid & Rafael Schmidt, 2007. "Nonparametric inference on multivariate versions of Blomqvist’s beta and related measures of tail dependence," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 66(3), pages 323-354, November.
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