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A new multivariate transform and the distribution of a random functional of a Ferguson-Dirichlet process

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

Abstract

A new multivariate transformation is given, with various properties, e.g., uniqueness and convergence properties, that are similar to those of the Fourier transformation. The new transformation is particularly useful for distributions that are difficult to deal with by Fourier transformation, such as relatives of the Dirichlet distributions. The new multivariate transformation of the Dirichlet distribution can be expressed in closed form. With this result, we easily show that the marginal of a Dirichlet distribution is still a Dirichlet distribution. We also give a closed form for the filtered-variate Dirichlet distribution. A relation between the new characteristic function and the traditional characteristic function is given. Using this multivariate transformation, we give the distribution, on the region bounded by an ellipse, of a random functional of a Ferguson-Dirichlet process over the boundary.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:111:y:2004:i:1:p:77-95
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. 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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    1. 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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