Today I Learned: arsinh(x)

A few weeks ago I was looking for a function that would squeeze variables with large magnitude, but behaved like the identity function close to zero. After a couple of days without finding something that suited me, I gave up.

Luckily for me, however, Kaiser Fung blogged a couple days ago about a weird scale used on an article and one of the commenters pointed out that arsinh(x) (that is, the inverse of the sinh(x) function) works like a "pseudo-log" (the poster themselves use this name for a different function described on the same comment), and best of all, fits my need for something close to the identity around zero. Talk about coincidences.

Well, this post makes it public to the world that even after a whole Engineering degree and nearing 10 years in Statistics/ML, I had never studied nor used hyperbolic functions before. One day I'll find out why and where I should use sinh and cosh, but for today, adding arsinh(x) to my data visualization toolkit is enough.

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