10. Notes on the Scaled Dirichlet Distribution

  1. Vera Pawlowsky-Glahn2 and
  2. Antonella Buccianti3
  1. Gianna Serafina Monti1,
  2. Glòria Mateu-Figueras2 and
  3. Vera Pawlowsky-Glahn2

Published Online: 28 JUL 2011

DOI: 10.1002/9781119976462.ch10

Compositional Data Analysis: Theory and Applications

Compositional Data Analysis: Theory and Applications

How to Cite

Monti, G. S., Mateu-Figueras, G. and Pawlowsky-Glahn, V. (2011) Notes on the Scaled Dirichlet Distribution, in Compositional Data Analysis: Theory and Applications (eds V. Pawlowsky-Glahn and A. Buccianti), John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119976462.ch10

Editor Information

  1. 2

    Department of Computer Science and Applied Mathematics, University of Girona, Spain

  2. 3

    Department of Earth Sciences, University of Florence, Italy

Author Information

  1. 1

    Department of Statistics, University of Milan-Bicocca, Italy

  2. 2

    Department of Computer Science and Applied Mathematics, University of Girona, Spain

Publication History

  1. Published Online: 28 JUL 2011
  2. Published Print: 23 SEP 2011

ISBN Information

Print ISBN: 9780470711354

Online ISBN: 9781119976462

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Keywords:

  • notes on the scaled Dirichlet distribution;
  • compositional data - definition parts of some whole;
  • genesis of scaled Dirichlet distribution - best known distribution, for categorical data modelling;
  • Bayesian inference, and Dirichlet distribution - natural conjugate prior for multinomial likelihood;
  • properties of scaled Dirichlet distribution - probabilistic properties, classical and Aitchison representations;
  • membership in exponential family - densities of multidimensional exponential families;
  • measures of location and variability - and mode of Dirichlet distribution;
  • Dirichlet distribution, exhibiting - maximum form of independence compatible with unit sum constraint;
  • Aitchison geometry, a scaled Dirichlet distribution - perturbing the Dirichlet one;
  • special algebraic-geometric structure of simplex - scaled Dirichlet density, translation of a Dirichlet density

Summary

This chapter contains sections titled:

  • Introduction

  • Genesis of the Scaled Dirichlet Distribution

  • Properties of the Scaled Dirichlet Distribution

  • Conclusions

  • Acknowledgements

  • References