AW: Re: Corresponding function to given values...
- To: mathgroup at smc.vnet.net
- Subject: [mg36022] AW: [mg36005] Re: Corresponding function to given values...
- From: Matthias.Bode at oppenheim.de
- Date: Tue, 13 Aug 2002 05:22:45 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Hello Sven,
1. If you just want a function that "accurately" hits your values use
InterpolatingPolynomial[{yourdata}, x]
2. If you suspect that your data should nicely fit some distribution try the
appropriate tests; see Statistics`HypothesisTests`.
3. If you have a smart idea about your data (e. g. your data represent
temperature over time in a fermentation vessel) look for known (technical)
functions that describe your type of process: You will probably find more
input variables than just time.
4. Most interesting case:
We know next to nothing about the real nature of the data but we want to
find out in a very broad approach if the data coincide (more or less) with
values of some known mathematical function. Wolfram Research gives us:
http://functions.wolfram.com/ where they have 37,366 functions as of
today.....
It would be interesting to know if there is something like a
"FunctionFinder" which - given some (learned) guesses may help us to
identify functions that more or less replicate our data. From these we may
get some clue about the nature of the process underlying our data by
checking which phenomena these functions usually describe. Hopefully.
Best regards,
Matthias Bode
Sal. Oppenheim jr. & Cie. KGaA
Koenigsberger Strasse 29
D-60487 Frankfurt am Main
GERMANY
Tel.: +49(0)69 71 34 53 80
Mobile: +49(0)172 6 74 95 77
Fax: +49(0)69 71 34 95 380
E-mail: matthias.bode at oppenheim.de
Internet: http://www.oppenheim.de
-----Ursprüngliche Nachricht-----
Von: Sven Richter [mailto:Sven.Richter at unibw-muenchen.de]
Gesendet: Montag, 12. August 2002 09:34
An: mathgroup at smc.vnet.net
Betreff: [mg36005] Re: Corresponding function to given values...
Ok, I thank you for your help. The values {1,2},{2,4},{3,9} were only an
example. And the 2 in the first pair should actually be an 1.... But
this doesn't matter since you understood the problem. I also knew the
problem, that I have to give something like a "model" for the
function... Unfortunatly, I have no idea, how the function looks like. I
thought, that Matematica is maybe able to compare these values with
known functions (and combinings of them). But it looks like there is no
way...
Anyway, the real pairs of values are:
{{0.5,3.45058},{1,5.3352},{1.5,6.9328},{1.8,7.306},{1.9,7.2962},{2,
7.2163},{2.5,5.8877},{3,3.7307},{3.4464,2.0000},{4,0.6928},{5,0.04575}}
At first, I thougt that the function is something like the density
function of the standard normal distribution... Thus, I tried the
following function (and lots of modifications):
(a + e*x)\(2[Pi] Exp[0.5 (c*x^d + b)^2])
Unfortunatly, the result wasn't very accurate...
I know, that this is not longer a problem a Mathematica, but I just
wanted to let you know...
Anyway, I thank you all for your help.
Regards,
Sven