Multivariate Guassian Distribution

 I want to learn Multivariate Gussian distribution so I written the following code.*I am implementing following formula 

 

Iam expecting this type of plot

Where I am doing mistake?

 

clear all
clc

% Taking two guassian random variables
x=randn(1000,1);
y=randn(1000,1);

X=[x y];
X=X';
d=size(X,1);

% find means of x,y
mx=mean(x);
my=mean(y);

mumat=[mx my]';
mumat=repmat(mumat,1,size(X,2));

Dif_mat=X-mumat;
% The above step (Dif_mat) is (X-mu) in the formula

cov_mat=cov(X'); % covariance matrix
det_cv=det(cov_mat); % det of cov matrix
inv_cov=inv(cov_mat); % inverse of cov matrix

% scale term before exp in forumala
scale=((2*pi)^(d/2))*sqrt((abs(det_cv))); 
scale=inv(scale);

% Mahabolis distance in formula 
MB=Dif_mat'*cov_mat*Dif_mat;

% find the final probability
p=scale*exp((-1/2)*MB);

surf(x,y,p)

 

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You're really trying to do two things here. The first is, you have some random data and you want to fit it to a multivariate normal distribution. Your approach to this part works, although it can be streamlined:

 

n = 1000; d=2;
X = randn(n,2);

Get mean and covariance:

mumat=mean(X);
cov_mat=cov(X);

The second part is plotting the resulting distribution. Here you need a regular grid for your variables, not the random values you generated above:

x = -3:.2:3; y = -3:.2:3;
[X,Y] = meshgrid(x,y);
X = X-mumat(1); Y = Y-mumat(2);

Combine X and Y in a way that each row represents one 2D variable.

Z = [X(:) Y(:)];

Now calculate the probabilities.

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