function aic = AIC(SS,N,K)
%AIC Akaike's Information Criterion for curve-fitting model comparison
% AIC(SS,N,K) where SS is the sum of squared residuals (as returned by e.g. lsqcurvefit)
% N is the number of data points and K is the number of coefficients.
% Computes and returns the corrected AIC score for the model.
% The model with the lowest AIC value is the best fit.
% References: (1) Motulsky, H. and Christopoulos, A. (2003) Fitting models to biological data using
% linear and nonlinear regression. A practical guide to curve fitting. Graphpad Software Inc., San Diego CA.
% (2) Akaike, H. (1974) "A new look at the statistical model identification." IEEE Transactions on Automatic Control, AC-19, 716-723
% (3) Hurvich, C. M., and Tsai, C-L. (1989). Regression and time series model selection in small samples. Biometrika, 76, 297-307.
% [the AIC correction]
% NOTE: this computes AIC from sum-of-squares (SS), and thus uses SS as
% an esimator for the maximum likelihood; when actually fitting
% distributions using MLE, then use AICL instead!
% Mark Humphries 11/10/2004
K = K + 1; % additional degree-of-freedom is model!
% raw AIC
aic = N .* log(SS./N) + 2 .* K;
% apply correction in case N close to K
aic = aic + (2.*K.*(K+1)) ./ (N - K - 1);