Let $\chi$ be a random probability measure chosen by a Dirichlet process on $(\mathbb{R}, \mathscr{B})$ with parameter $\alpha$ and such that $\int x\chi(dx)$ turns out to be a (finite) random variable. The main concern of this paper is the statement of a suitable expression for the distribution function of that random variable. Such an expression is deduced through an extension of a procedure based on the use of generalized Stieltjes transforms, originally proposed by the present authors in 1978.
Publié le : 1990-03-14
Classification:
Dirichlet probability distribution function,
Dirichlet process,
distribution of random functionals,
generalized Stieltjes transform,
62G99,
62E15,
60K99,
44A15
@article{1176347509,
author = {Cifarelli, Donato Michele and Regazzini, Eugenio},
title = {Distribution Functions of Means of a Dirichlet Process},
journal = {Ann. Statist.},
volume = {18},
number = {1},
year = {1990},
pages = { 429-442},
language = {en},
url = {http://dml.mathdoc.fr/item/1176347509}
}
Cifarelli, Donato Michele; Regazzini, Eugenio. Distribution Functions of Means of a Dirichlet Process. Ann. Statist., Tome 18 (1990) no. 1, pp. 429-442. http://gdmltest.u-ga.fr/item/1176347509/