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A stochastic equation for the law of the random Dirichlet variance

Author

Listed:
  • Epifani, I.
  • Guglielmi, A.
  • Melilli, E.

Abstract

This paper shows some new results concerning the law of the random variance V of a Dirichlet process P, expressed as the solution of a stochastic equation involving the squared difference between two independent copies of the mean of P. An explicit solution of this equation is obtained via the Zolotarev transform of V. Moreover, we discuss the correspondence between the distribution of the variance and the parameter of the Dirichlet process with given total mass.

Suggested Citation

  • Epifani, I. & Guglielmi, A. & Melilli, E., 2006. "A stochastic equation for the law of the random Dirichlet variance," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 495-502, March.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:5:p:495-502
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    References listed on IDEAS

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    1. Nils Hjort & Andrea Ongaro, 2005. "Exact Inference for Random Dirichlet Means," Statistical Inference for Stochastic Processes, Springer, vol. 8(3), pages 227-254, December.
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    Cited by:

    1. 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.
    2. Dickey, James M. & Jiang, Thomas J. & Kuo, Kun-Lin, 2013. "Distribution of functionals of a Ferguson–Dirichlet process over an n-dimensional ball," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 216-225.

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