Gnuplot fitting
I want to fit the following data:
70 0.0429065
100 0.041212
150 0.040117
200 0.035018
250 0.024366
300 0.02017
350 0.018255
400 0.015368
to the following function which is combination of an exponantial and a gaussian functions:
$ f(x)= a1*(a2* exp(-x/T2e)+ exp(-(x/T2g)**2))
$ fit f(x) 'data' via a1,a2,T2e,T2g
But it keeps giving me the following results:
a1 = 0.0720021 +/- 0.04453 (61.84%)
a2 = 0.310022 +/- 0.9041 (291.6%)
T2e = 63291.7 +/- 2.029e+07 (3.206e+04%)
T2g = 252.79 +/- 32.36 (12.8%)
While when I try to fit it separetly to
$ g(x)=b* exp(-(x/T2g)**2)
$ fit g(x) 'data' via b,T2g
I get
b = 0.0451053 +/- 0.001598 (3.542%)
T2g = 359.359 +/- 16.89 (4.701%)
and
$ S(x)=S0* exp(-x/T2e)
$ fit S(x) 'data' via S0,T2e
gives:
S0 = 0.057199 +/- 0.003954 (6.913%)
T2e = 319.257 +/- 38.17 (11.96%)
I already tried to set the initial values but it didn't change the results.
Does anybody know what is wrong? Thank you,
Ok, you can see an exponential decay with a hump which could be a Gaussian.
The approach, how I got to a fit: first, exclude the datapoints 100 and 150 and fit the exponental and then set a Gaussian approximately at 170.
You probably don't get a good fit, because at least the Gaussian peak is shifted by some value x1.
With the code:
### fitting
reset session
$Data <<EOD
70 0.0429065
100 0.041212
150 0.040117
200 0.035018
250 0.024366
300 0.02017
350 0.018255
400 0.015368
EOD
a = 0.055
T2e = 310
b = 0.008
x1 = 170
T2g = 54
Exponential(x) = a*exp(-x/T2e)
Gaussian(x) = b*exp(-((x-x1)/T2g)**2)
f(x) = Exponential(x) + Gaussian(x)
fit f(x) $Data u 1:2 via a,b,x1,T2e,T2g
plot $Data u 1:2 w lp pt 7, f(x) lc rgb "red"
### end of code
You'll get:
a = 0.0535048 +/- 0.00183 (3.42%)
b = 0.00833589 +/- 0.001006 (12.06%)
x1 = 170.356 +/- 5.664 (3.325%)
T2e = 315.114 +/- 12.94 (4.106%)
T2g = 54.823 +/- 12.13 (22.12%)
