A Collection of Fitting Functions

A collection of fitting functions for various distributions.

Description

%
% 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
%

• MATLAB release: MATLAB 6.1 (R12.1)

[Aaron Clarke]

Works great and the graphs are aesthetically pleasing.

[Rafi Levi]

 

[P Z]

1D Gaussian works great. 2D Gaussian gives significantly different (and more poorly fit) results than other EM implementations I've tried, e.g., Netlab and Weka.

[Fabio Labra]

Works great and has neat graphics. First time I find a function for ML fitting of laplace distribution.

[M C]

Great stuff! Seems really usable, at least the 1D functions.

[Richard Xiao]

great tools for gaussian 1D fittings, thanks.

[Shane Lin]

really good stuff. thanx

[seth man]

I'm finished my take home test with this stuff

[J Lansey]

Wow! thats perfect, the author is an EXPERT coder. Proffesionall i'd say.
Thanks!

[Leif Adelow]

Missing subroutine or toolbox containing 'mvnrnd'.

??? Undefined function or variable 'mvnrnd'.

[pau soler]

Thank you for such great routines.

[John Finan]

I hit a snag that cost me an hour and I thought I would try to save someone else the time. Disclaimer: I have only been playing with this code for a few hours. I have NOT read it all and I don't fully understand it.

The snag involved plotting the output from a fit of mixed gaussians in one dimension. When I generated the data using build_mix_gaussian, a plot was created. Then, fit_mix_gaussian would plot into that figure without any trouble.

However, when I was using my own data, I didn't run build_mix_gaussian first and the output from fit_mix_gaussian got all messed up.

Here's the change I made in the very last line of fit_mix_gaussian to fix it.

% plot_mix_gaussian( u,sig,t );
plot_mix_gaussian( u,sig,t,X );

Comments from the author or other users are very welcome.

[venkatesh siva]

thanks

[Yong-Jun Cho]

thanks!

[Todd Arnold]

The provided files are an excellent source for EM based Matlab work.

[Thomas Clark]

This submission requires the statistics toolbox, in order to use the 2D gaussian fit (line 32, build_mix_2D_gaussian.m)

[mahdi poorakbari]

 

[Harish Viswanathan]

 

[Elli Dolev]

Hello there,
I found your application very usfull and I winder if it is possible to use it and to ask you one question please.
Thank you,
Elli

[Om Ken]

Guys, i use Randraw function to generate data randomly from a truncated normal distribution, but when i tested the generated data if they have come from a Normal distribution (not truncated), the hypothesis was rejected. which means that the data can not be assumed to have come from a Normal distribution, If I use the Normal distribution to fit my collected data using for example dfittool tool box, I get a mean and sigma values , when I use them to genera data from the randraw function with using (y = randraw('normaltrunc', [0, +inf, mu, sigma], 1, 1e5), the data obtained do not follw a normal distribution. so what i need is some kind of distribution fitting tool that can fit my original field collected data to a left Truncated normal distribution and give me the right parameters , i.e. mu and sigma
regards

[c a]

Had similar problem to John Finan above and used same fix. However have other problem with fit_mix_gaussian: it seems to be sensitive to magnitude to data. Using data scaled from appr. -0.7 to 5 it gives me a fit which is incorrect (data is skewed in some manner I have not identified). Changing the magnitude of the input vector via multiplication by some constants causes it to not converge for > 50k iterations.

Rather than systematically determine the failure modes, is there any info on requirements on input vector, such as normalization, etc.? I see normalization required for LSE's but for gaussian?

Thanks