histogram of Bivariate Normal distribution plot

I have values from a monte carlo simulation. now i am supposed to plot the results using a bivariate gaussian.

Since it is experimental data on a specific topic, i was given the empirical formula of the PDF(x,y):

and this is the plot I should get( obviously it will be different depending on my data):

I don't understand how to implement the plot

This is the part of the code where I calculate STD, means:

N=1000
x=detriti_coord(:,1); %along-track direction  Gaussian
y=detriti_coord(:,2); %cross-track direction  Gaussian

mu_x=mean(x);
mu_y=mean(y);

sigma_x= sqrt(1/N*sum((x-mu_x).^2)) 
sigma_y= sqrt(1/N*sum((y-mu_y).^2))

Delta_x= x-mu_x;
Delta_y= y-mu_y;
rho_xy= sum(Delta_x.*Delta_y)/(N*sigma_x*sigma_y);

Answer 1

[Yash]

Hi Giovanni,

I understand that you are facing issues while making a 3 dimensional histogram of a PDF function.

Since you have clearly mentioned that you are facing issues in the implementation of the plot, I am assuming that your calculations are correct. From the problem statement, it seems that you want to plot the histograms of x and y values from the experimental data.

To achieve this, you can use the "hist3" function. You can refer the to the documentation for "hist3"at the following link: https://www.mathworks.com/help/stats/hist3.html.

If you want to plot the rho_xy as well with the histogram, you can use the "surf" function. You can refer the to the documentation for "surf" at the following link: https://www.mathworks.com/help/matlab/ref/surf.html

Note that to show both the plots in the same axes, you need to use "hold on".

I am using random values to show an example:

x = randi(10, 100, 1);    %100*1 matrix of random doubles ranging from 0 to 10
y = randi(10, 100, 1);

hist3([x y]);
hold on


arraySize = 100;
sigma = 50;

x1 = linspace(0,10,arraySize);     %100 points between 0 to 10
[X,Y] = meshgrid(x1,x1);           %setting up for the x and y axis for the surf plot

z = fspecial("gaussian", arraySize, sigma);    % gaussian distribution

z = z*(3/max(z,[],'all'));                     % scaling from 0 to 3

ans = 3

surf(X,Y,z);

hold off

Hope this helps!