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arXiv · 2201.05950

Refined normal approximations for the Student distribution

Frédéric Ouimet
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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.

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Frédéric Ouimet. 2022-01-16. Refined normal approximations for the Student distribution. https://doi.org/10.7153/jca-2022-20-03

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