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Distributional properties of means of random probability measures

Author

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  • Antonio Lijoi
  • Igor Prünster

Abstract

The present paper provides a review of the results concerning distributional properties of means of random probability measures. Our interest in this topic has originated from inferential problems in Bayesian Nonparametrics. Nonetheless, it is worth noting that these random quantities play an important role in seemingly unrelated areas of research. In fact, there is a wealth of contributions both in the statistics and in the probability literature that we try to summarize in a unified framework. Particular attention is devoted to means of the Dirichlet process given the relevance of the Dirichlet process in Bayesian Nonparametrics. We then present a number of recent contributions concerning means of more general random probability measures and highlight connections with the moment problem, combinatorics, special functions, excursions of stochastic processes and statistical physics.

Suggested Citation

  • Antonio Lijoi & Igor Prünster, 2009. "Distributional properties of means of random probability measures," Carlo Alberto Notebooks 120, Collegio Carlo Alberto.
    • Handle: RePEc:cca:wpaper:120
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    File URL: https://www.carloalberto.org/wp-content/uploads/2018/11/no.120.pdf
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    Cited by:

    1. Antonio Lijoi & Igor Prünster, 2014. "Discussion of “On simulation and properties of the stable law” by L. Devroye and L. James," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(3), pages 371-377, August.
    2. Antonio Lijoi & Igor Pruenster, 2009. "Models beyond the Dirichlet process," ICER Working Papers - Applied Mathematics Series 23-2009, ICER - International Centre for Economic Research.
    3. Julyan Arbel & Riccardo Corradin & Bernardo Nipoti, 2021. "Dirichlet process mixtures under affine transformations of the data," Computational Statistics, Springer, vol. 36(1), pages 577-601, March.

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