Re: st: Transformation of variable with pos/neg values via asinh

[David Hoaglin <dchoaglin@gmail.com>]

Nick,

I'm in favor of "if it helps."

I would classify volume and gamma distributions as "amounts," however,
not "balances."

As a quirky example related to the cube root, I like the relation
between the gauges of shotguns (e.g., 10, 12, and 14) and the
diameters of their barrels.  Before the diameters were standardized,
the gauge of a shotgun (or a musket) was equal to the number of lead
balls of the barrel diameter needed to make a weight of 1 pound.
Thus, the gauge is proportional to the reciprocal cube root of the
barrel diameter.

The Wilson-Hilferty approximation is supported by solid analysis.

David Hoaglin

On Tue, Nov 19, 2013 at 7:37 AM, Nick Cox <njcoxstata@gmail.com> wrote:
> Nothing depends on my one-off terminology. Perhaps "inputs" and
> "outputs" capture my meaning better.
>
> The leading examples I know of for cube roots are
>
> volumes go to lengths
>
> and
>
> gammas go to Gaussians (to a good approximation; "Wilson-Hilferty" is
> a known incantation here)
>
> and everything else is a matter of "if it helps".
> Nick
> njcoxstata@gmail.com
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