How to fit data to a Gaussian distribution

Hi there, I'm quite new of MatLab and thus I hope you'll be patient with me.

I need to fit a given distribution (an actual one I generated from subjects) to its theorical Gaussian and get the R square value.

The Model (Gaussian distribution) I use is: Y=Amplitude*exp(-0.5*((X-Mean)/SD)^2) Amplitude is the height of the centre of the distribution in Y units. Mean is the X value at the centre of the distribution. SD is a measure of the width of the distribution, in the same units as X.

Rules for initial values Parameter Initial value Rule Amplitude 1.0 *YMAX No constraint MEAN 1.0 *(Value of X at YMAX) No constraint SD 0.1 *(XMAX-XMIN) Must be > 0.0

I use to do that with GraphPad and SPSS but I'd like to be able to do that in MatLab too. I need some good soul to tel me, step by step, how to do that in MatLab.... Please

Answer 1

[Matt J]

Study the documentaion for FMINSEARCH and consider the following

 fminsearch(@(p) norm( p(1).*exp(-0.5.*((X(:)-p(2))./p(3)).^2) -Y(:)), p0)

[Lorenzo]

Sorry but I don't get it :,(

[Matt J]

Here's a simpler example where I fit the slope p(1) and intercept p(2) of a line:

    >>x=0:.01:1; 
    y=2*x+1;  
    initialguess=[0,0];

    >> [pfit,residual]=fminsearch(@(p) norm(p(1)*x+p(2)-y) , initialguess)

    pfit =

        2.0000    1.0000

    residual =

       2.1512e-04

In reality, you would use POLYFIT to fit a line or any other polynomial, of course. This was just an example.

[Lorenzo]

Thanks, I'll try to see if I can make it working (as I said I am really neieve of MatLab).

Answer 2

[Tom Lane]

Similar question in the newsgroup: http://www.mathworks.com/matlabcentral/newsreader/view_thread/325685