A Collection of Fitting Functions

A collection of fitting functions for various distributions.

%
% 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.
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% 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)
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% 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".
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% 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
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% 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.
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% 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
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% these routines fit and plot the results of the parameters of:
% random distribution of random amount of gaussians with random parameters
%