Exact bounds on the closeness between the Student and standard normal distributions
Document Type
Article
Publication Date
1-1-2015
Abstract
© 2015 EDP Sciences, SMAI. 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 (SDp) 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 SDp and SDq with q> p. Comparisons with known bounds are made.
Publication Title
ESAIM - Probability and Statistics
Recommended Citation
Pinelis, I.
(2015).
Exact bounds on the closeness between the Student and standard normal distributions.
ESAIM - Probability and Statistics,
19, 24-27.
http://doi.org/10.1051/ps/2014014
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/8642