IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v120y2013icp216-225.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X13001115
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2013.05.013?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Nils Lid Hjort & Andrea Ongaro, 2006. "On the distribution of random Dirichlet jumps," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 61-92.
    3. 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.
    4. Lancelot F. James & Antonio Lijoi & Igor Prünster, 2006. "Distributions of Functionals of the two Parameter Poisson-Dirichlet Process," ICER Working Papers - Applied Mathematics Series 29-2006, ICER - International Centre for Economic Research.
    5. Antonio Lijoi & Igor Prunster, 2009. "Models beyond the Dirichlet process," Quaderni di Dipartimento 103, University of Pavia, Department of Economics and Quantitative Methods.
    6. 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.
    7. Eliardo G. Costa & Carlos Daniel Paulino & Julio M. Singer, 2023. "Optimal sample size for estimating the mean concentration of invasive organisms in ballast water via a semiparametric Bayesian analysis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(1), pages 57-74, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:120:y:2013:i:c:p:216-225. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.