学生分布的精细正态近似

Journal of classical analysis Pub Date : 2022-01-16 DOI:10.7153/jca-2022-20-03

Frédéric Ouimet

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引用次数: 2

摘要

本文给出了学生分布的一个局部极限定理。我们用它来改进Shafiei & Saberali(2015)中给出的学生生存函数的正态近似，并在四个近似级别上推导出相应最大误差的渐近界。作为推论，学生分布的百分比(或分位数)的近似值是根据标准正态分布的百分比获得的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Refined normal approximations for the Student distribution

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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