## Distribution of a random functional of a Ferguson-Dirichlet process over the unit sphere.(English)Zbl 1192.60040

Summary: T. J. Jiang, J. M. Dickey and K.-L. Kuo [Stochastic Processes Appl. 111, No. 1, 77–95 (2004; Zbl 1070.60014)] gave the multivariate $$c$$-characteristic function and showed that it has properties similar to those of the multivariate Fourier transformation. We first give the multivariate $$c$$-characteristic function of a random functional of a Ferguson-Dirichlet process over the unit sphere. We then find out its probability density function using properties of the multivariate $$c$$-characteristic function. This new result would generalize that given by T. J. Jiang [Stat. Probab. Lett. 12, No. 3, 263–265 (1991; Zbl 0745.60048)].

### MSC:

 6e+11 Characteristic functions; other transforms 6.2e+16 Exact distribution theory in statistics

### Keywords:

ferguson-Dirichlet process; c-characteristic function

### Citations:

Zbl 1070.60014; Zbl 0745.60048
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