Refined normal approximations for the Student distribution

@article{Ouimet2022RefinedNA,
  title={Refined normal approximations for the Student distribution},
  author={Fr{\'e}d{\'e}ric Ouimet},
  journal={Journal of Classical Analysis},
  year={2022}
}
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. 
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