What is the vintage of this result?

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It turns out that there is a very cute lower bound on the skewness g_1 of a strictly positive set of data having given mean and sd:

g_1 > \mu/\sigma + \sigma/\mu.

For reasons outlined in this PubPeer post, I have to suppose this is a very old result. But the authors claim to have done a diligent literature search, and I have no reason to doubt them.

So I’m wondering if a citation might come to mind for any of you who read Fisher’s writings over breakfast in the original Sanskrit — lookin’ at you, @Stephen @R_cubed and @Sander!

2 Likes
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I have now posted this on CrossValidated, with a bounty.

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A 100-point bounty has expired uncollected after 1 week, and the question remains without an accepted answer. There’s ample reason to believe now at least that this result is little-known.

Meanwhile, I have used the result in this PubPeer comment, to develop an objective rationale for why this plot was in poor taste:
Qi-2021-Fig2b