Refined normal approximations for the Student distribution
Statistics Theory
2022-07-29 v2 Probability
Statistics Theory
Abstract
In this paper, we develop a local limit theorem for the Student distribution. We use it to improve the normal approximation of the Student survival function given in Shafiei & Saberali (2015) and to derive asymptotic bounds for the corresponding maximal errors at four levels of approximation. As a corollary, approximations for the percentage points (or quantiles) of the Student distribution are obtained in terms of the percentage points of the standard normal distribution.
Cite
@article{arxiv.2201.05950,
title = {Refined normal approximations for the Student distribution},
author = {Frédéric Ouimet},
journal= {arXiv preprint arXiv:2201.05950},
year = {2022}
}
Comments
9 pages, 1 figure