How do I curve fit the data set

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Prajwal Magadi
Prajwal Magadi on 29 Jul 2023
Commented: Sam Chak on 29 Jul 2023
Hello all,
I'm facing difficulty in fitting the data.
The red ones are from the data set, and I want to fit that as like blue one (Experimental Data). How can I do that. I have also attached the data set for your reference.
Thank You.
  2 Comments
Sam Chak
Sam Chak on 29 Jul 2023
What is the mathematical function of the blue curve? Is it a skewed normal distribution function?
Can you also suggest some candidate functions for fitting into the red data? Look up some Kernel functions.
Red data seems to have discontinuities at multiple intervals. Is it acceptable to have a piecewise function to fit the data?
Prajwal Magadi
Prajwal Magadi on 29 Jul 2023
The blue curve is also a data set from an experimental obervation.
The red data is from the simulation.
And I have no idea of the function type of blue data.

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Accepted Answer

Sam Chak
Sam Chak on 29 Jul 2023
Not sure if this is what your want. But you can try finding the best math function to fit.
data = load('curve_fit.mat');
x = data.theta_degree';
y = data.x';
skewEqn = 'a/(sqrt(2*pi))*exp(- b*(x - c)^2)*((1/2)*(1 + erf(e*(x - c)/sqrt(2)))) + d';
fo = fitoptions('Method', 'NonlinearLeastSquares',...
'Lower', [ 0, 0, 5, 0, 0.1],... % {a, b, c, d, e}
'Upper', [100, 1, 20, 10, 1.0],...
'StartPoint', [50 0.5 10 5 0.5]);
ft = fittype(skewEqn, 'options', fo);
[yfit, gof] = fit(x, y, ft)
yfit =
General model: yfit(x) = a/(sqrt(2*pi))*exp(- b*(x - c)^2)*((1/2)*(1 + erf(e*(x - c)/sqrt(2) ))) + d Coefficients (with 95% confidence bounds): a = 85.15 (84.38, 85.93) b = 0.003494 (0.003423, 0.003564) c = 7.162 (7.116, 7.209) d = 2.461 (2.241, 2.681) e = 0.3845 (0.3752, 0.3937)
gof = struct with fields:
sse: 9.7227e+04 rsquare: 0.9063 dfe: 9995 adjrsquare: 0.9062 rmse: 3.1189
plot(yfit, x, y)
grid on, xlabel('\theta'), ylabel('x')
legend('Data', 'Fitted Skew Dist Fcn')

More Answers (1)

Alex Sha
Alex Sha on 29 Jul 2023
@Prajwal Magadi, one more function:
Sum Squared Error (SSE): 75571.6557870726
Root of Mean Square Error (RMSE): 2.74902993412354
Correlation Coef. (R): 0.962878352853849
R-Square: 0.927134722394541
Parameter Best Estimate
--------- -------------
y0 3.57509887406416
a 10210313.7484567
xc 17.1109591760412
w1 18.7010167618592
w2 -1.38399464317597
w3 -1.49504622174935
  3 Comments
Alex Sha
Alex Sha on 29 Jul 2023
Hi, your data chart looks like peak-type function chart, so just try some typical peak functions, "Asym2Sig" function, shown above, gives more better outcomes.
Sam Chak
Sam Chak on 29 Jul 2023
Hi @Alex Sha, thanks for sharing the information about the Asymmetric Double Sigmoidal function. I don't have Origin Pro, and I have never seen many of those functions before.

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