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A measure of dependence between two compositions

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Author

Summary, in English

We consider the problem of describing the correlation between two compositions. Using a bicompositional Dirichlet distribution, we calculate a joint correlation coefficient, based on the concept of information gain, between two compositions. Numerical values of the joint correlation coefficient are calculated for compositions of two and three components. We also present an estimator of the joint correlation coefficient for a sample from a bicompositional Dirichlet distribution. Two confidence intervals are also presented and we examine their empirical confidence coefficient using Monte Carlo study. Finally we apply the estimator to a data set analysing the correlation between the 1967 and 1997, and the 1977 and 1997 compositions of the government gross domestic product for the 50 U.S. states and District of Columbia.

Publishing year

2012

Language

English

Pages

451-461

Publication/Series

Australian & New Zealand Journal of Statistics

Volume

54

Issue

4

Document type

Journal article

Publisher

Wiley-Blackwell

Topic

  • Probability Theory and Statistics

Keywords

  • correlation
  • Dirichlet distribution
  • empirical confidence coefficient
  • Fraser information
  • joint correlation coefficient
  • simplex

Status

Published

ISBN/ISSN/Other

  • ISSN: 1467-842X