How to fit multivariate pdf and cdf from data
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supernoob
el 30 de Jun. de 2018
Comentada: Tim Fulcher
el 24 de Dic. de 2021
I have a set of simulated data from a Monte Carlo simulation which gives me a bivariate distribution. I can plot the results using histogram2, and I expect the results to be bivariate gaussian. How can I properly fit this 'empirical' data to get a normalized pdf and cdf which I can then integrate over to get some confidence intervals?
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Jeff Miller
el 1 de Jul. de 2018
You don't need a bivariate histogram to fit the bivariate normal--just use the sample means and covariance matrix. Here's an example:
% Let's say your data are in an n,2 matrix called xy.
% Here is one randomly generated to use in the example.
muXY = [100, 200];
sigmaXY = [15^2, 5^2; 5^2, 20^2];
xy = mvnrnd(muXY,sigmaXY,10000);
% Here is your bivariate histogram:
figure; histogram2(xy(:,1),xy(:,2));
% Now estimate the parameters of the best-fitting Gaussian:
xybar = mean(xy);
xycovar=cov(xy);
% Plot the best-fitting bivariate pdf:
xsteps = min(xy(:,1)):1:max(xy(:,1)); % Adjust with step sizes appropriate for your
ysteps = min(xy(:,2)):1:max(xy(:,2)); % x and y values.
[X,Y] = meshgrid(xsteps,ysteps);
F = mvnpdf([X(:) Y(:)],xybar,xycovar); % Note that xybar and xycovar are used here.
F = reshape(F,length(ysteps),length(xsteps));
figure; surf(xsteps,ysteps,F);
caxis([min(F(:))-.5*range(F(:)),max(F(:))]);
xlabel('x'); ylabel('y'); zlabel('Probability Density');
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dpb
el 30 de Jun. de 2018
Editada: dpb
el 30 de Jun. de 2018
They're in the BinCounts property of the object or you can just use the old histcounts2.
ADDENDUM
Ah, ok. I've not tried in Matlab, seems a definite lack of no prepared function indeed...
Attach your data and I'll try to see if I can give it a go later on...btw, you'll probably get much better fit using the raw data than histogram bin counts.
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