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 how many points are the best for curve fitting?
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tony_lincoln

USA
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Posted - 09/02/2006 :  12:06:21 AM  Show Profile  Edit Topic  Reply with Quote  View user's IP address  Delete Topic
Dear friends,

If I have one curve of 200 points and fit it with one exponential equation(Y=A(1-exp(tau*x))), I will get one Tau value. If I cut this curve, and throw the last 50 points, just fit the curve of first 150 points, I will get another Tau. Same, if I just use the first 30 points of this curve and try to fit it, I will get the 3rd Tau --- All of these three Tau values are not the same at all: The 1st one can be 0.03, the 2nd one can be 0.1 and the 3nd one can be 0.2! --- which one is correct? What is the best point number for expoential fitting? Do you have any paper or literature for this question?
Thanks a lot.
Best wishes.
Tony

rlewis

Canada
253 Posts

Posted - 09/02/2006 :  12:59:44 AM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
Perhaps your data is not adequately defined by a single exponential decay ....
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tony_lincoln

USA
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Posted - 09/02/2006 :  7:04:47 PM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
Thank you Lewis,

I will try to fit using biexponential equation instead of single exponential equation. The theoretical model was already there and was prooved that it was correct during the last 20 years. The model says that you can use either biexponential or single exponential equation for different case.

single exponential equation
Y=A0 + A(1-exp(tau*x)) which has 3 parameters,
or biexponential equation: Y=A0 + A1(1-exp(tau1*x)) + A2(1-exp(tau2*x))
which has 5 parameters.


If I use the correct equation, I should get the same Tau value if I fit the curve which was cut away the last 50, 100 or 150 points. Is this correct?

Thanks.
Tony
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tony_lincoln

USA
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Posted - 09/03/2006 :  3:18:48 PM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
Dear friends,

Unfortunately I did not get the same Tau value when the curve was cut away the last 50, 100 or 150 points. However, during the last 20 years, it has been proved that mono-exponential or bi-exponential function is the correct solution for this kind of data.
Following Jeremy's suggestion, I think that this might mean:
1) My data has systematic errors in it
2) I am losing accuracy in my calculation of exp(tau*x) for large x

My question now is, how to get rid of systematic errors? How to prevent losing ccuracy in my calculation of exp(tau*x) for large x?
Thanks.
TOny
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larry_lan

China
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Posted - 09/03/2006 :  11:12:34 PM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
Hi Tony:

Curve fitting is a statistical procedure base on all of your input data. So if your data is sorted and you "Cut" the curve by removing the last or first 50 points, how can you make sure that the new data can represent the original curve?

So if you have a large data set and you want to re-sample it, maybe you should pick the points randomly, or pick them by fixed interval, instead of just throw the last 50 points.

If you don't mind, would you please send your .OPJ to tech@originlab.com and we can have a look on it.

Thanks

Larry
OriginLab GZ Office
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zachary_origin

China
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Posted - 09/03/2006 :  11:47:51 PM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
I have generated the data using the formula with A=0.8,tau=0.3 and added 5% white noise, where X is from 0.1 to 30 with step 0.1. Then I do fitting with the data for different points using BoxLucas1 function, which conforms with your formula.
The result is as following:
For first 50 points, a=0.91809 b = -0.2928
For the following 200 points,a=0.86718 b=-0.30419
For the last 50 points, a=0.78903 b=-0.30493
For all the points, a=0.91809 b=-0.2928
(b represents tau in your formula).

From the results, we can seen that though there are some differences between different points, the difference is not so large.

So can you send your data to us via tech@originlab.com

Zachary
OriginLab GZ Office
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tony_lincoln

USA
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Posted - 09/07/2006 :  11:53:43 AM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
Hi Larry and Zachary,

Thanks a lot for your words which are helpful. I agree with Larry --- if I remove the last 50 points, it will not represent the original curve. If I want to re-sample it, you should pick the points by fixed interval.
I will try this later.
I am sending one data set with step 0.5 (using email address jug@stowers-institue.org), also the xls file with the fitting result that I made. Maybe with different function (BoxLucas1, mono-expoential, bi-exponential or other function), you will get different result.
Thanks a lot.
Tony
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larry_lan

China
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Posted - 09/07/2006 :  11:55:15 PM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
Hi tony:

I have tried your data and email you.

Thanks

Larry
OriginLab GZ Office
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