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Abstract:
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The random functional of the Ferguson-Dirichlet process has been subjected to research for decades. Univariate c-characteristic functions, which were first given by Jiang (1988), have been shown to have many properties similar to those of the traditional univariate characteristics function. These alternative c-characteristic functions are very useful, especially for those cases that are difficult to manage using the traditional characteristic function. Examples can be seen in Jiang (1988, 1991). Jiang, Dickey, and Kuo (2004) further extended them to be the multivariate c-characteristic functions. In this paper, we first give inversion formulas for these c-characteristic functions. Using them, we give a general expression of the random functional of the Ferguson-Dirichlet process. The exact prob. density functions of the random moments of some Ferguson-Dirichlet process are also given.
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