What is the vintage of this result?

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!


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