I have never used commonmean (or agm) so am happy for whatever change is
agreed upon.
If we are worried about backwards compatibility then we could assign both
commonmean & agm to the agreed definition to start with.
As I understand it the current geomean definition will handle arguments
that include -ve numbers, whereas gmean won't?
We could define agm so that it chooses the correct form depending the
length of the arg as an alternative to having 2 separate verbs.
agm=: 3 :0
select. #y
case. <: 2 do.
([: {. (%:@*/ , -:@+/) ^: _) y
case. do.
([: {: (mean,geomean) ^:_) y
end.
)
On Fri, Sep 2, 2016 at 4:09 AM, Martin Kreuzer <[email protected]> wrote:
> [On Chris' suggestion this thread was moved here from "Chat" forum as
> there are programming topics involved ...]
>
> Hm, this debate about the term "common mean" seems to be 1.5 decades old
> ...
>
> I'm directing this post especially (but not exclusively) to
>
> - Chris Burke and
> - Ric Sherlock
>
> as from looking at the "trunk" it seems that these gentlemen have been the
> sole maintainers of the '/addons/stats/base/univariate.ijs' script.
> (Thanks Martin Neitzel for showing me the way.)
>
> Additional problem however is that the term in question is used in various
> other places and discussions on the site.
>
> -----
>
> After I did some more reading on the subject (calculating different means)
> may I suggest this:
>
> [1]
> In this context, drop the name "common mean" altogether.
> It is used for other stuff (in descriptive statistics e.g. when comparing
> separate datasets).
>
> [2]
> Use "agm" instead.
> This is what is meant (limit of two convergent sequences), and seems to be
> the accepted abbreviation, see e.g.
> http://mathworld.wolfram.com/Arithmetic-GeometricMean.html
> (Gauss is said to have coined agM, short for 'arithmetisch-geometrisches
> Mittel'.
> AGM is used to evaluate Elliptic Integrals, which in turn may be used to
> calculate e.g. the perimeter of an ellipse.
> The AGM approach has also been used to formulate fast convergent
> algorithms to calculate Pi.)
>
> NB. This should take _two_ arguments as input;
> NB. it will show strange results when used on more than two arguments
> agm=: [: {. (%:@*/ , -:@+/) ^: _
>
> or (maybe better)
>
> NB. restrained
> agm=: 3 : '{: (-:@+/,%:@*/)^:_ a,b [''a b''=. y'
>
> NB. seems alright (twice same argument)
> agm 1
> 1
> NB. intended use (two arguments)
> agm 1,%%:2
> 0.847213
> NB. failing with error message
> agm 1,2,3
> |length error: agm
> | {:(-:@+/,%:@*/)^:_ a,b['a b' =.y
>
> [3]
> Use "agmx" or "cmean" or "cm" (short for Compound Mean = extended AGM)
> when there are more than two values in the argument list.
>
> With
>
> NB. arithmetic mean
> amean=: +/ % #
> NB. geometric mean
> gmean=: amean &.: ^.
>
> agmx=: [: {: (amean,gmean) ^:_
>
> -----
>
> Please let me know of
>
> - your thoughts regarding the proposed changes;
> - ways to improve on the verbs mentioned.
>
> Thanks
> -M
>
>
> At 2016-08-04 20:31, you wrote:
>
> Entering "with the *exact phrase" "*common mean" on the following link
>>
>> http://www.jsoftware.com/forumsearch
>>
>> produced 20 messages:
>>
>> http://www.jsoftware.com/cgi-bin/forumsearch.cgi?all=&exa=co
>> mmon+mean&one=&exc=&add=&sub=&fid=&tim=0&rng=0&dbgn=1&mbgn=
>> 1&ybgn=1998&dend=31&mend=12¥d=2016
>>
>> On Thu, Aug 4, 2016 at 12:04 PM, Martin Kreuzer <[email protected]>
>> wrote:
>>
>> > Hi all -
>>
>> > Working my way through "/addons/stats/base/univariate.ijs" I covered
>> the
>> > basics up to (var) and (stddev).
>>
>> > Q:
>> > Could somebody point me to a worked example illustrating the use of
>> > (commonmean)..?
>> > commonmean=: [: {. (%:@*/ , -:@+/) ^: _
>> > (This is not so much about the programming but about the general concept
>> > of that term, as I'm only so far aware of 'common arithmetic mean'.
>> That's
>> > the reason I put it here in Chat.)
>>
>> > Thanks.
>> > -M
>>
>>
>>
>> --
>> (B=)
>> ----------------------------------------------------------------------
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>>
>
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