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

作者：Dickey James M; Jiang Thomas J^*; Kuo Kun Lin

来源：Journal of Multivariate Analysis, 2013, 120: 216-225.

DOI：10.1016/j.jmva.2013.05.013

• Characteristic function
• Dirichlet distribution
• Ferguson-Dirichlet process
• Random functional
• Spherically symmetric distribution

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.

• 出版日期2013-9