×

zbMATH — the first resource for mathematics

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:
60E10 Characteristic functions; other transforms
62E15 Exact distribution theory in statistics
PDF BibTeX XML Cite
Full Text: DOI EMIS EuDML