Curve fitting to get gamma curve parameter

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Putra A on 6 Apr 2013
Commented: Torsten on 6 Mar 2018
Dear Forum Member.
I want to fit a curve to gamma like curve with current data that i have.
i need to get shape and scale parameter from the data that i assume have a gamma intensity curve.
Here is the grey level as (Y)
Columns 1 through 17
150 149 151 157 163 169 174 176 177 177 177 181 185 186 185 184 181
Columns 18 through 24
176 173 171 169 167 168 168
and the index is
Columns 1 through 14
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Columns 15 through 24
15 16 17 18 19 20 21 22 23 24
if i create the plot it will be like this
i want to assume the graph as gamma curve, how to get the shape and scale parameter for this curve if i only have x and y ?
new image :
Thank you :)

Tom Lane on 9 Apr 2013
I'm not sure what you mean by a gamma curve. If you mean a scalar multiple of a curve with the same form as a gamma probability density function, here's an example using nlinfit from the Statistics Toolbox:
function main
y = [150 149 151 157 163 169 174 176 177 177 177 181 ...
185 186 185 184 181 176 173 171 169 167 168 168];
x = 1:24;
p = nlinfit(x,y,@f,[1 10 150])
plot(x,y,'bo',x,f(p,x),'r-')
end
function y = f(abc,x)
a = abc(1); b = abc(2); c = abc(3);
y = c * x.^(a-1) .* exp(-x/b) / (b^a * gamma(a));
end
Putra A on 10 Apr 2013
Ok nice, thank you for the answer tom :)

bym on 6 Apr 2013
If you have the statistics toolbox, you can use:
gamfit()
bym on 7 Apr 2013
Yes, I thought your question pertained to statistics not image processing. You can use
lsqcurvefit()
to fit a nonlinear curve, but it appears from your plot that your data does not follow a power law

Shariefa Shaik on 6 Mar 2018
Why [1 10 150] values only
Torsten on 6 Mar 2018
These are initial guesses for the parameters to be determined, not data points.