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<p>It has been observed empirically that the sum of medians of skewed distributions is sometimes smaller than the median of their sum. To date, however, there has been no conclusive formal demonstration of this fact. This note continues an initial investigation in Van Zwet (Stat Neerl 33(1):1–5, 1979). It establishes a number of median inequalities, for example that the sum of medians of right-skewed distributions is smaller than the median of the sum, for a specific definition of skewness, and that the product of the medians of positive symmetric distributions is greater than the median of their product.</p>

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A note on the median of skewed distributions

  • 期刊论文

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  • 发表日期：

    2026年5月14日

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  • Tim Hunter

摘要

It has been observed empirically that the sum of medians of skewed distributions is sometimes smaller than the median of their sum. To date, however, there has been no conclusive formal demonstration of this fact. This note continues an initial investigation in Van Zwet (Stat Neerl 33(1):1–5, 1979). It establishes a number of median inequalities, for example that the sum of medians of right-skewed distributions is smaller than the median of the sum, for a specific definition of skewness, and that the product of the medians of positive symmetric distributions is greater than the median of their product.