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Re: st: Transformation of variable with pos/neg values via asinh
From
Nick Cox <[email protected]>
To
"[email protected]" <[email protected]>
Subject
Re: st: Transformation of variable with pos/neg values via asinh
Date
Tue, 19 Nov 2013 13:16:50 +0000
In case it's unclear to anyone
(a) Cube roots can be useful for transforming amounts, not least if
the amount could be zero.
(b) Cube roots -- much more unusually -- extend to negative quantities
too, just as (-2)(-2)(-2) = -8.
The two positions
Nick
[email protected]
On 19 November 2013 13:13, David Hoaglin <[email protected]> wrote:
> 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 <[email protected]> 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
>> [email protected]
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