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Exponential functionals and means of neutral-to-the-right priors

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  • Ilenia Epifani

Abstract

The mean of a random distribution chosen from a neutral-to-the-right prior can be represented as the exponential functional of an increasing additive process. This fact is exploited in order to give sufficient conditions for the existence of the mean of a neutral-to-the-right prior and for the absolute continuity of its probability distribution. Moreover, expressions for its moments, of any order, are provided. For illustrative purposes we consider a generalisation of the neutral-to-the-right prior based on the gamma process and the beta-Stacy process. Finally, by resorting to the maximum entropy algorithm, we obtain an approximation to the probability density function of the mean of a neutral-to-the-right prior. The arguments are easily extended to examine means of posterior quantities. The numerical results obtained are compared to those yielded by the application of some well-established simulation algorithms. Copyright Biometrika Trust 2003, Oxford University Press.

Suggested Citation

  • Ilenia Epifani, 2003. "Exponential functionals and means of neutral-to-the-right priors," Biometrika, Biometrika Trust, vol. 90(4), pages 791-808, December.
    • Handle: RePEc:oup:biomet:v:90:y:2003:i:4:p:791-808
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    Cited by:

    1. Antonio Lijoi & Igor Pruenster & Stephen G. Walker, 2008. "Posterior analysis for some classes of nonparametric models," ICER Working Papers - Applied Mathematics Series 05-2008, ICER - International Centre for Economic Research.
    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. Antonio Lijoi & Igor Pruenster, 2009. "Distributional Properties of means of Random Probability Measures," ICER Working Papers - Applied Mathematics Series 22-2009, ICER - International Centre for Economic Research.
    4. Konstancja Bobecka & Jacek WesoĊ‚owski, 2007. "The Dirichlet Distribution and Process through Neutralities," Journal of Theoretical Probability, Springer, vol. 20(2), pages 295-308, June.
    5. Angelos Dassios & Junyi Zhang, 2023. "Exact Simulation of Poisson-Dirichlet Distribution and Generalised Gamma Process," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-21, June.
    6. Salminen, Paavo & Vostrikova, Lioudmila, 2019. "On moments of integral exponential functionals of additive processes," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 139-146.
    7. Arbel, Julyan & Lijoi, Antonio & Nipoti, Bernardo, 2016. "Full Bayesian inference with hazard mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 359-372.

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