A sharper bound of the Hotelling–Solomons inequality

Pub Date : 2024-07-09 DOI:10.1002/sta4.710
Yuzo Maruyama
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Abstract

The original Hotelling–Solomons inequality states that an upper bound of the absolute difference between the mean and median, standardised by the standard deviation, is 1. However, in this paper, we introduce a new bound that depends on the sample size, which is strictly smaller than 1.
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霍特林-索洛蒙斯不等式的更尖锐约束
最初的 Hotelling-Solomons 不等式指出,平均值与中位数之间的绝对差值(以标准差标准化)的上限为 1。然而,在本文中,我们引入了一个取决于样本量的新上限,它严格小于 1。
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