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Distribution of functionals of a Ferguson–Dirichlet process over an n-dimensional ball

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  • Dickey, James M.
  • Jiang, Thomas J.
  • Kuo, Kun-Lin

Abstract

The c-characteristic function has been shown to have properties similar to those of the Fourier transformation. We now give a new property of the c-characteristic function of the spherically symmetric distribution. With this property, we can easily determine whether a distribution is spherically symmetric. The exact probability density function of the random mean of a spherically symmetric Ferguson–Dirichlet process with parameter measure over an n-dimensional spherical surface and that over an n-dimensional ball are given. We further give the exact probability density function of the random mean of a Ferguson–Dirichlet process with parameter measure over an n-dimensional ellipsoidal surface and that over an n-dimensional ellipsoidal solid.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:120:y:2013:i:c:p:216-225
    DOI: 10.1016/j.jmva.2013.05.013
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    References listed on IDEAS

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    1. Jiang, Thomas J. & Dickey, James M. & Kuo, Kun-Lin, 2004. "A new multivariate transform and the distribution of a random functional of a Ferguson-Dirichlet process," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 77-95, May.
    2. Jiang, Tom J., 1991. "Distribution of random functional of a Dirichlet process on the unit disk," Statistics & Probability Letters, Elsevier, vol. 12(3), pages 263-265, September.
    3. Torkel Erhardsson, 2008. "Non‐parametric Bayesian Inference for Integrals with respect to an Unknown Finite Measure," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(2), pages 369-384, June.
    4. 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.
    5. 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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