Abstract
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.
Citation
T. Cacoullos. V. Papathanasiou. S. A. Utev. "Variational Inequalities with Examples and an Application to the Central Limit Theorem." Ann. Probab. 22 (3) 1607 - 1618, July, 1994. https://doi.org/10.1214/aop/1176988616
Information