Exact bounds on the closeness between the Student and standard normal distributions
Pinelis, Iosif1
1 Department of Mathematical Sciences, Michigan Technological University, Houghton, 49931 Michigan, USA
ESAIM: Probability and Statistics, Tome 19 (2015), pp. 24-27.

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. Comparisons with known bounds are made.

Reçu le :
DOI : 10.1051/ps/2014014
Classification : 62E17, 60E15, 62E20, 62E15
Mots clés : Student’s distribution, standard normal distribution, Kolmogorov distance, total variation distance, probability inequalities
Pinelis, Iosif 1

1 Department of Mathematical Sciences, Michigan Technological University, Houghton, 49931 Michigan, USA 
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Pinelis, Iosif. Exact bounds on the closeness between the Student and standard normal distributions. ESAIM: Probability and Statistics, Tome 19 (2015), pp. 24-27. doi : 10.1051/ps/2014014. http://www.numdam.org/articles/10.1051/ps/2014014/

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