# Exact bounds on the closeness between the Student and standard normal distributions

@inproceedings{Pinelis2011ExactBO, title={Exact bounds on the closeness between the Student and standard normal distributions}, author={Iosif Pinelis}, year={2011} }

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.

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