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The Dirichlet Distribution and Process through Neutralities

Author

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  • Konstancja Bobecka

    (Politechnika Warszawska)

  • Jacek Wesołowski

    (Politechnika Warszawska)

Abstract

A new characterization of the Dirichlet distribution, based on the notion of complete neutrality and a regression version of neutrality, is derived. It unifies earlier characterizations by James and Mosimann (Ann. Stat. 8, 183–189, 1980) and by Seshadri and Wesołowski (Sankhyā, A 65, 248–291, 2003). Also new results on identification of the Dirichlet process in the class of neutral-to-the-right processes are obtained. The proof of the main result makes an extensive use of the method of moments.

Suggested Citation

  • Konstancja Bobecka & Jacek Wesołowski, 2007. "The Dirichlet Distribution and Process through Neutralities," Journal of Theoretical Probability, Springer, vol. 20(2), pages 295-308, June.
    • Handle: RePEc:spr:jotpro:v:20:y:2007:i:2:d:10.1007_s10959-007-0069-y
    DOI: 10.1007/s10959-007-0069-y
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    References listed on IDEAS

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    1. ROLIN, Jean-Marie, 1992. "Some useful properties of the Dirichlet process," LIDAM Discussion Papers CORE 1992007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Rameshwar D. Gupta & Donald St. P. Richards, 2001. "The History of the Dirichlet and Liouville Distributions," International Statistical Review, International Statistical Institute, vol. 69(3), pages 433-446, December.
    3. Rolin, J.M., 1992. "Some Useful Properties on the Dirichlet Process," Papers 9202, Catholique de Louvain - Institut de statistique.
    4. Ilenia Epifani, 2003. "Exponential functionals and means of neutral-to-the-right priors," Biometrika, Biometrika Trust, vol. 90(4), pages 791-808, December.
    5. Lo, Albert Y., 1991. "A characterization of the Dirichlet process," Statistics & Probability Letters, Elsevier, vol. 12(3), pages 185-187, September.
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