Title

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

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