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frankwagner
France
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 Posted - 02/13/2007 : 09:48:16 AM
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Hello,
is there a possibility to define another merit function for the nonlinear fitter? I mean for normally distributed measurements one fits by minimizing the Chi2 (eventuelly weighted).
I have data that obeys the binominal distribution and would like to fit it.
Thus I would need to redefine the merit function that has to be minimized. Can I do this in origin? Does somebody know another program that does it?
Thanks a lot for your help,
Frank
Origin Version (Select Help-->About Origin): 7.5 SR6
Operating System: Win XP |
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Mike Buess
USA
3037 Posts |
Posted - 02/13/2007 : 10:49:19 AM
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Hi Frank,
I assume you mean binomial rather than binominal. Chi^2 is merely a measure of the deviation of predicted values from measured values and should work for any model. Why doesn't it work as merit function for binomial distribution?
BTW, duplicate posting is an unnecessary waste of the reader's time.
Mike Buess
Origin WebRing Member |
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frankwagner
France
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Posted - 02/15/2007 : 09:15:19 AM
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Hi Mike,
the reason why Chi^2 is usually a good merit function is because usual measurements are normally distributed around the average value. The probability to realize a measurement assuming a known value of y is expressed by the normal distribution shifted to the average of the measurement y_a. Thus the average is the best estimator for the value of y. For curve fitting, the y are generated by the fit model y_f(x,b) with a model parameter b. The probability that has to be optimized (realize all measurement points simultaneaously) is then given by something proportional to
Exp( -(y_f(x1,b)-y_a(x1))^2/sigma^2(x1) ) * Exp ( ... at position x2)
Maximising this expression by varying b results in minimizing:
(y_f(x1,b)-y_a(x1))^2/sigma^2(x1)+(y_f(x2,b)-y_a(x2))^2/sigma^2(x2)+...
this is the weighted Chi^2, or, if you set all sigma^2 values to the same value, it is proportional to the simple Chi^2.
We measure probabilities, thus the values are not normally distributed and the estimator is not given by the average... The initial gaussian of the normal distribution has to be replaced by the appropriate binomial distribution and Chi^2 is no longer a valid merit function.
However, using Origin instead of programming something by myself may safe time and make sure that the errors of the fit parameter b are correctely calculated. (In reality I would like to compare several models with 2 to 9 fit parameters)
FW |
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easwar
USA
1965 Posts |
Posted - 02/15/2007 : 11:14:54 AM
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Hi Frank,
The minimization algorithm in Origin works only on minimizing chi-sqr and there is no option to minimize a different entity.
We will need to look into this for a future version. Thank you for t he input.
Easwar
OriginLab
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definition of another merit function for fitting