Exact bounds on the closeness between the Student and standard normal distributions
Statistics Theory
2017-01-17 v2 Probability
Statistics Theory
Abstract
Upper bounds on the Kolmogorov distance (and, equivalently in this case, on the total variation distance) between the Student distribution with p degrees of freedom (SD_p) and the standard normal distribution are obtained. These bounds are in a certain sense best possible, and the corresponding relative errors are small even for moderate values of p. The same bounds hold on the closeness between SD_p and SD_q with q>p.
Keywords
Cite
@article{arxiv.1101.3328,
title = {Exact bounds on the closeness between the Student and standard normal distributions},
author = {Iosif Pinelis},
journal= {arXiv preprint arXiv:1101.3328},
year = {2017}
}
Comments
Comparisons with the corresponding results by Shimizu; Cacoullos, Papathanasiou, and Utev; and Bourguin and Tudor are added