| Issue |
ESAIM: PS
Volume 19, 2015
|
|
|---|---|---|
| Page(s) | 24 - 27 | |
| DOI | https://doi.org/10.1051/ps/2014014 | |
| Published online | 17 March 2015 | |
Exact bounds on the closeness between the Student and standard normal distributions
Department of Mathematical Sciences, Michigan Technological
University, Houghton,
49931
Michigan,
USA
ipinelis@mtu.edu
Received:
13
June
2013
Revised:
19
May
2014
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.
Mathematics Subject Classification: 62E17 / 60E15 / 62E20 / 62E15
Key words: Student’s distribution / standard normal distribution / Kolmogorov distance / total variation distance / probability inequalities
© EDP Sciences, SMAI, 2015
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