| Re: geometric mean? [message #21724 is a reply to message #21626] |
Fri, 08 September 2000 09:59  |
noymer
Messages: 65
Registered: June 1999
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Member |
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In article <39B8B345.FDF4E45D@dkrz.de>,
Martin Schultz <martin.schultz@dkrz.de> wrote:
> Hi Andrew,
>
> I couldn't find such a routine either so I decided to hack it
> together using the algorithm you suggest but including some error
> cehcking and more caution with range limits or negative values. You
> can find geomean.pro on my web pages:
>
http://www.mpimet.mpg.de/~schultz.martin/idl/html/libmartin_ schultz.html
>
> Cheers,
> Martin
>
Dear Martin,
Thanks!!!
You include checking for negative values, which would mess
up the ALOG function.
Since I am taking geometric means of rates that are by
definition positive, I did not think of negative numbers.
There is a problem, though...
Someone please correct me if this is wrong; I'm not 100% sure.
The way I implemented the geometric mean was not the DEFINITION of
the geomean, but rather a computational SHORTCUT.
The DEFINITION goes something like:
GEOMEAN(Arr)=(PROD(Arr))^(1/n), where n is the number of elements,
and PROD is the product operator. Logging both sides gets rid of the
nasty "nth root" (i.e. ^(1/n)) and turns the product into a sum, which
is also nice. Then exponentiating un-transforms the log.
Clearly we can't log any negative number, but we can product a
bunch of numbers and then take an nth root of the result. And if there
are zero or an even number of negative numbers there will be a real
nth root, hence (I guess), the geomean would exist.
I don't know what the convention is with negative numbers, and
it doesn't affect me because I am using positive numbers, but maybe
someone out there knows:
(1) Is geomean by convention undefined if any numbers in the set
are negative?
(2) Is geomean always the positive nth root? geomean of -2 and -2
is +2?
Cheers,
Andrew
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