How Matlab compute marginals

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Fabio Garofalo 2016-6-21

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https://ww2.mathworks.cn/matlabcentral/answers/291275-how-matlab-compute-marginals

评论： Fabio Garofalo 2016-6-21

Hi, I'm computing the marginals for a given distribution (a Gaussian with a given covariance) by using the following code

clear all;
close all;
format shorte;
n=100000;
s=[[2,1];[1,3]];
x=chol(s)*randn(2,n);
figure
h=scatterhist(x(1,:),x(2,:));hold(h(1,2),'on');
xi=linspace(-10,10,1001);
plot(h(1,2),xi,1/sqrt(2*pi*s(1,1))*exp(-xi.^2/(2*s(1,1))));
figure
histogram(x(1,:),100,'normalization','pdf','facecolor','w');hold on;
plot(xi,1/sqrt(2*pi*s(1,1))*exp(-xi.^2/(2*s(1,1))));

however it seems that the actual x-marginal does not coincide with the theoretical one, that for the case I'm considering is a probabilistic Gaussian with zero mean and sqrt(s(1,1)) standard deviation.

Am I wrong or there is something else?

Thanks in advance, F