fitting scatter plot with two-dimensional normal distribution (Gaussian)?

Hi everyone,

I need to fit the attached scatter plot to 2-D normal distribution (Gaussian), as i undertood the expected result should be like ellipsoid, i tried so many think but i could reach what i want! e.g: when i tried the gaussian fit i got like straight line crossing y axis at zero...

this photo generated from x,y of 566*2 matrix.

thanks in advance

Answer 1

[Jeff Miller]

You can calculate the 5 parameters of the best estimated bivariate normal directly from the x and y values: mean & sd of each variable and Pearson correlation. What else do you want?

Answer 2

[buthayna alnaalwa]

thanks, can you help me how to caluclate those parameters, still new user!

[buthayna alnaalwa]

also the point is for me i need every time to fit one normal distribution Gaussian , by having two Gaussians i will have like ellipsoidal shape as i understood,,,, but when i tried to fit one gaussian it gave only straight line so no ellipsoidal shape as intersect

[Jeff Miller]

MATLAB has nice functions to calculate the parameter, such as:

% Assume your data are in x,y
muX = mean(x);
sigmaY = std(y);
rhoXY = corr(x,y);

I don't really understand what you want, but your comments about ellipsoids suggest that you are trying to plot the bivariate distribution. The usual way to do that is with a surface plot. Here is a good example from Image Analyst: Previous Answer

You can use your mu & sigma values, computed as above, and adjust xl and yl to give ranges appropriate for the ranges of your x and y

Answer 3

[buthayna alnaalwa]

thanks for your help