MATLAB: How do we plot a bivariate normal distribution from one side

3d plotsdensity

Dear all

I plot the following bivariate distribution

 mu = [0 0];
Sigma = [.25 .3; .3 1];
x1 = -3:.2:3; x2 = -3:.2:3;
[X1,X2] = meshgrid(x1,x2);
F = mvnpdf([X1(:) X2(:)],mu,Sigma);
F = reshape(F,length(x2),length(x1));
surf(x1,x2,F);
caxis([min(F(:))-.5*range(F(:)),max(F(:))]);
axis([-3 3 -3 3 0 .4])
xlabel('x1'); ylabel('x2'); zlabel('Probability Density');

My question is how do I plot the joint density from the vantage point of x1 or x2? So I want to obtain a 2D graph that shows x1 (or x2) on the x-axis and the density values on the y-axis

Any help is greatly appreciated.

Thanks in advance

Best Answer

You can plot the marginal distribution of x or y separately, using whatever variance and mean corresponds to it (page 4 of this link ).

For you, I think x1 has a sigma^2 of 0.25, and a mean of 0, so you can plot it like:

x = -3:.2:3;
density = normpdf(x, 0, sqrt(0.25));
plot(x, density);

Related Solutions

MATLAB: Bivariate Normal Distribution different for expression and mvnpdf()

Hello Aishwarya,

The problem here is that the array x is 2x31 and does not have every possible combination of an element of X1 and an element of X2, which is 2x961. The method 2 code below fixes that by implementing the same idea as in method 1,

   X = [X1(:) X2(:)];

For method 2 to be correct you need the factor in front to be to the +1/2 power, since you have already put the factor into the denominator.

    mu = [0,0];
    sigma =  [0.5 0.8; 0.8 2.0];
    x1 = -3:0.2:3;
    x2 = -3:0.2:3;
    X = [x1; x2]
    [X1,X2] = meshgrid(x1,x2);
    X = [X1(:) X2(:)];
    y = mvnpdf(X,mu,sigma);
    y = reshape(y,length(x1),length(x2));
    figure(1)
    surf(X1,X2,y)
    xlabel('x')
    ylabel('y')
    zlabel('Bivariate Gaussian Distributions')
   
    % method 2       
    mu = [0;0];
    covar =  [0.5 0.8; 0.8 2.0];
    x1 = -3:0.2:3;
    x2 = -3:0.2:3;
    [X1,X2] = meshgrid(x1,x2);
    X = [X1(:), X2(:)]';
    arg = sum((X-mu).*(pinv(covar)*(X-mu)));
    y2 = 1/(2*pi*(det(covar))^(1/2)) * exp(-(1/2)*arg);
    y2 = reshape(y2,size(X1));
    figure(2)
    surf(X1,X2,y2)
    xlabel('x')
    ylabel('y')
    zlabel('Bivariate Gaussian Distributions')
   
    max(max(abs(y-y2)))
   
    ans = 1.8041e-16

MATLAB: When I try to 3d plot the code, the plot comes out empty what should I add to fix this problem

To Mohsen

Actually, I don't know what exactly you want to do. But There are some problems in your code such as variable dimension(size), matrix(array) calculation...

check this out. hope this will be helpful for you.

      F = [-40:20:40];
      x = linspace(0.1,0.8,length(F));
      y = linspace(0.1,0.4,length(F));
      sigma_p = @(x,y) F./(.8.*x.*y);
      sigma_mx = @(x,y) (F.*y)./(1./12.*(x).*(y).^3);
      sigma_my = @(x,y) (F.*x)./(1./12.*(y).*(x).^3);
      sigma_net = @(x,y) sigma_p(x,y) + sigma_mx(x,y) + sigma_my(x,y);
      figure
      plot3(x, y, sigma_net(x,y))

Best Answer

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MATLAB: Bivariate Normal Distribution different for expression and mvnpdf()

MATLAB: When I try to 3d plot the code, the plot comes out empty what should I add to fix this problem

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