English

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.

Keywords

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

R2 v1 2026-06-24T08:51:19.597Z