Upper bounds for the distance in variation between an arbitrary probability measure and the standard normal one are established via some integrodifferential functionals including information. The results are illustrated by gamma- and $t$-distributions. Moreover, as a by-product, another proof of the central limit theorem is obtained.
Publié le : 1994-07-14
Classification:
Distance in variation,
Stein's identity,
central limit theorem,
60F15,
60F05
@article{1176988616,
author = {Cacoullos, T. and Papathanasiou, V. and Utev, S. A.},
title = {Variational Inequalities with Examples and an Application to the Central Limit Theorem},
journal = {Ann. Probab.},
volume = {22},
number = {4},
year = {1994},
pages = { 1607-1618},
language = {en},
url = {http://dml.mathdoc.fr/item/1176988616}
}
Cacoullos, T.; Papathanasiou, V.; Utev, S. A. Variational Inequalities with Examples and an Application to the Central Limit Theorem. Ann. Probab., Tome 22 (1994) no. 4, pp. 1607-1618. http://gdmltest.u-ga.fr/item/1176988616/