Hi,
I understand that you would like to fit a custom curve c(x) using the data you have sampled "x" and "q". You can use the code given below to find the value of "rho" which best fits the curve "c".
% Here I have used some sample values for "x" and "q":
x = [0.81;0.91;0.13;0.91;0.63;0.098;0.28;0.55; ...
0.96;0.96;0.16;0.97;0.96];
q = [0.17;0.12;0.16;0.0035;0.37;0.082;0.34;0.56; ...
0.15;-0.046;0.17;-0.091;-0.071];
% Calling 'fittype' for the pdf of the Cauchy distribution written in 'testing_cauchy' function.
ft = fittype("testing_cauchy(x, rho)");
f = fit(x,q,ft) % This command will output the value of all fitting parameters (rho in our case)
% with 95% confidence bounds
The following function should be in a MATLAB function file on the path.
function y = testing_cauchy(x, rho) % implementation of cauchy function, all other variables are treated as fitting parameters
gamma = 0.001; % change according to usage
y = zeros(size(x));
for i= 1:length(x)
y(i) = gamma/(((x(i)-rho)^2+gamma^2)*pi);
end
Hope this helps!
