How to plot a joint pdf of 2 independent continuous variables?

Hey guys, I have data series of 2 continuous random variables, both are independent, I want to plot their joint pdf. I tried using the meshgrid and surf commands but I am not able to succeed. I tried the following code:

load('tut1_3_indpXY.txt')
X = corr(tut1_3_indpXY)
Y = tut1_3_indpXY'
A = Y(1,:)
B = Y(2,:)
M1 = mean(A)
M2 = mean(B)
S1 = std(A)
S2 = std(B)
N1 = pdf('Normal',A,M1,S1)
N2 = pdf('Normal',B,M2,S2)
N1T = N1'
MIN1 = min(A)
MAX1 = max(A)
MIN2 = min(B)
MAX2 = max(B)
I1 = linspace(MIN1,MAX1,200)
I2 = linspace(MIN2,MAX2,200)
[P,Q] = meshgrid(I1,I2)
R = N1T*N2
surf(P,Q,R)

[Kapil Varne]

Here is the code:

load('tut1_3_indpXY.txt')

X = corr(tut1_3_indpXY)

Y = tut1_3_indpXY'

A = Y(1,:)

B = Y(2,:)

M1 = mean(A)

M2 = mean(B)

S1 = std(A)

S2 = std(B)

N1 = pdf('Normal',A,M1,S1)

N2 = pdf('Normal',B,M2,S2)

N1T = N1'

MIN1 = min(A)

MAX1 = max(A)

MIN2 = min(B)

MAX2 = max(B)

I1 = linspace(MIN1,MAX1,200)

I2 = linspace(MIN2,MAX2,200)

[P,Q] = meshgrid(I1,I2)

R = N1T*N2

surf(P,Q,R)

[the cyclist]

Can you upload your text file, so we can try your code? Even better would be the MAT file with the variable.

Also, is there a reason you uploaded the code twice? Is there a difference?

Answer 1

[the cyclist]

Taking an admittedly quick look, shouldn't your joint pdf be

R = N1T.*N2

rather than what you have?

If you have an older version of MATLAB, you'll need to do

R = bsxfun(@mtimes,N1T,N2)

Answer 2

[Himanshu]

I tried to do the same thing, by the raw calculation of gaussian distribution,

But I am facing the below error

close all;
clear all;

% sigma of i is more that q, they are independent
sigma_q = 1;
sigma_i = sqrt(2);

x =-4:0.1:4;
y =-4:0.1:4;
[X, Y] = meshgrid(x,y);


pdf_i = (1/sqrt(2*pi)/sigma_i)*exp(-x.^2/(2*sigma_i^2));
pdf_q = (1/sqrt(2*pi)/sigma_q)*exp(-y.^2/(2*sigma_q^2));

joint = pdf_i.*pdf_q;

contour(X,Y,joint);

Error using contour
Z must be at least a 2x2 matrix.

surf(X,Y,joint);

[Himanshu]

Never Mind!

I was able to get the problem.

After doing the meshgrid, our x, y should the meshed ones, i.e. X, Y.

close all;
clear all;

% sigma of i is more that q, they are independent
sigma_q = 1;
sigma_i = sqrt(2);

x =-4:0.1:4;
y =-4:0.1:4;
[X, Y] = meshgrid(x,y);


pdf_i = (1/sqrt(2*pi)/sigma_i)*exp(-X.^2/(2*sigma_i^2));
pdf_q = (1/sqrt(2*pi)/sigma_q)*exp(-Y.^2/(2*sigma_q^2));

joint = pdf_i.*pdf_q;

%plot(x,joint);
figure();
contour(X,Y,joint);
grid("on");

figure();
surf(X,Y,joint);
grid("on");