Exact bounds on the closeness between the Student and standard normal distributions
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 January 2011
 arXiv:
 arXiv:1101.3328
 Bibcode:
 2011arXiv1101.3328P
 Keywords:

 Mathematics  Statistics Theory;
 Mathematics  Probability;
 Primary: 62E17;
 secondary: 60E15;
 62E20;
 62E15
 EPrint:
 Comparisons with the corresponding results by Shimizu