拟合函数--高斯，拉普拉斯，双高斯拟合

% This folder contains a collection of "fitting" functions. % (Some has demo options - the third section) % The GENERAL input to the functions should be samples of the distribution. % % for example, if we are to fit a normal distribution ('gaussian') with a mean "u" and varaince "sig"^2 % then the samples will distribute like: % samples = randn(1,10000)*sig + u % %fitting with Least-Squares is done on the histogram of the samples. % fitting with Maximum likelihood is done directly on the samples. % % % Contents of this folder % ======================= % 1) Maximum likelihood estimators % 2) Least squares estimators % 3) EM algorithm for estimation of multivariant gaussian distribution (mixed gaussians) % 4) added folders: Create - which create samples for the EM algorithm test % Plot - used to plot each of the distributions (parametric plot) % % % % % % Maximum likelihood estimators % ============================= % fit_ML_maxwell - fit maxwellian distribution % fit_ML_rayleigh - fit rayleigh distribution % (which is for example: sqrt(abs(randn)^2+abs(randn)^2)) % fit_ML_laplace - fit laplace distribution % fit_ML_log_normal- fit log-normal distribution % fit_ML_normal - fit normal (gaussian) distribution % % NOTE: all estimators are efficient estimators. for this reason, the distribution % might be written in a different way, for example, the "Rayleigh" distribution % is given with a parameter "s" and not "s^2". % % % least squares estimators % ========================= % fit_maxwell_pdf - fits a given curve of a maxwellian distribution % fit_rayleigh_pdf - fits a given curve of a rayleigh distribution % % NOTE: these fit function are used on a histogram output which is like a sampled % distribution function. the given curve MUST be normalized, since the estimator % is trying to fit a normalized distribution function. % % % % % Multivariant Gaussian distribution % ================================== % for demo of 1D mixed-gaussian fitting, run: fit_mix_gaussian % for demo of 2D mixed-gaussian fitting, run: fit_mix_2d_gaussian % % these routines fit and plot the results of the parameters of: % random distribution of random amount of gaussians with random parameters