In very broad terms, this looks like
a lot of parameters to fit a curve in two-space.
It looks as if you are modelling a two-peak curve.
There's presumably some physics behind this, but does
something more like
a4 * (a1*exp(-((x-a3)/a2)^2) + (1 - a1)*exp(-((x-a6)/a5)^2))
make sense as a model?
Nick
[email protected]
Andreas Aschbacher
> I am using a textfile with 364 rows as the following:
> /first column bar number,second column counts,these are
> results of an
> experiment in radioactive
> measurements /
> x y
> 1 84
> 2 77
> 3 87
> 4 56
> 5 69
> 6 57
> 7 67
> 8 40
> 9 46
> ....
> ....
>
>
> I know the result of our measurement if I fit the following function
> f(x) = a1*exp(-((x-a3)/a2)^2) + a4*exp(-((x-a6)/a5)^2) ,
> using x-column
> and y-column above :
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> results from fitting with f(x) above using LevenbergMarquard ::
> a1=~ 1138 a2= ~2.82 a3 = ~3.49 a4 = ~80.53 a5 = ~2.88
> a6 = ~7.99
> varianz of fit about ~0.148,because it isn't perfect
> Poisson-Statistik
> if I had perfect PoissonStatistik it would be in borders
> of : 0.925 to
> 1.075
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>
> but I don't get it by Stata.
> I can't reach it by varying the parameters.
> are there other possibilities to reach the aim.?
> thank you very much for help
>
>
> Andreas
>
> Here's the most important from the result-window :
>
> . do doubleGau� ' name of do-file
>
> . capture program drop nlexample
>
> . program nlexample
> 1. version 8
> 2. if "`1'" == "?" {
> 3. global S_1 "a1 a2 a3 a4 a5 a6"
> 4. global a1 = 1131
> 5. global a2 = 1
> 6. global a3 = 1
> 7. global a4 = 1
> 8. global a5 = 1
> 9. global a6 = 1
> 10. exit
> 11. }
> 12. replace `1' = $a1*exp(-((x-$a2)/$a3)^2) +
> $a4*exp(-((x-$a5)/$a6)^2)
> 13. end
>
> . twoway line y x
>
> . nl example y
> (obs = 364)
>
> Iteration 0: residual SS = 5.70e+07
> Iteration 1: residual SS = 5.58e+07
> Iteration 2: residual SS = 3.35e+07
> Iteration 3: residual SS = 3.32e+07
> Iteration 4: residual SS = 3.32e+07
> Iteration 5: residual SS = 3.32e+07
> Iteration 6: residual SS = 3.32e+07
> Iteration 7: residual SS = 3.32e+07
> Iteration 8: residual SS = 3.32e+07
> Iteration 9: residual SS = 3.32e+07
> .....................
> Iteration 77: residual SS = 1.48e+07
> Iteration 78: residual SS = 1.29e+07
> Iteration 79: residual SS = 2023443
> Iteration 80: residual SS = 315738.2
> Iteration 81: residual SS = 288846.4
> Iteration 82: residual SS = 288838.4
>
> Source | SS df MS
> Number of
> obs = 364
> -------------+------------------------------
> F( 2, 361)
> = 25371.18
> Model | 40599291 2 20299645.5
> Prob > F =
> 0.0000
> Residual | 288838.388 361 800.106339
> R-squared =
> 0.9929
> -------------+------------------------------
> Adj R-squared
> = 0.9929
> Total | 40888129.4 363 112639.475
> Root MSE =
> 28.28615
>
>
> Res. dev. =
> 3463.222
> (example)
> ------------------------------------------------------------
> ----------------------------
> y | Coef. Std. Err. t
> P>|t| [95%
> Conf.
> Interval]
> -------------+----------------------------------------------
> ----------------------------
> a1 | -76051.86 . .
> .
> . .
> a2 | -132556.8 . .
> .
> . .
> a3 | -11881.27 . .
> .
> . .
> a4 | 1131.814 5.267092 214.88 0.000
> 1121.456
> 1142.173
> a5 | 70.13886 .1312605 534.35 0.000
> 69.88072
> 70.39699
> a6 | 34.55454 .1859685 185.81 0.000
> 34.18882
> 34.92026
> ------------------------------------------------------------
> ------------------
> * Parameter a3 taken as constant term in model & ANOVA table
> (SEs, P values, CIs, and correlations are asymptotic
> approximations)
>
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
