%In physics, a three-parameter Lorentzian function is often used, as follows:
%  f(x;x0,?,I) = I/(1 + ( (x-x0)/? )^2)
% I: is the height of the peak.
% x0: is the location paremeter, specifying the location of the peak.
% ?: is the scale parameter which specifies the half-width at half-maximum (HWHM).
% ? is also equal to half the interquartile range and is sometimes called the probable error.

%If you would want,e. g., to ?t a Lorentzian y = a1/((x ? a2)^2 + a3) to a data set Xi, Yi, 
%you should define in MATLAB a function resulting in the sum of the squared residuals

% a(1)= I
% a(2)= x0
% a(3)= ?

function chisq = SupGau_devsum(a,X,Y)
%a
% a(1) = sigma_0
% a(2) = N;
% a(3) = x0
%SupGau = a(4)+1/(sqrt(2*pi)*a(1))*exp(-abs(X-a(3)).^a(2)/(2*a(1).^a(2)));% super gaussian 
% a(1) = base
% a(2) = A; amplitude
% a(3) = x0; center
% a(4) = D; sigma_0
% a(5) = N; 
SupGau = a(1)+a(2)*exp( -0.5*(abs(X-a(3))/(a(4))).^a(5) ); % super gaussian 
%X'
csq = (Y - SupGau).^2;
chisq = sum(csq); 
%csq
%chisq
return