how to plot joint distribtuion of 2 random variable having 1000 data - matlab

Question

here is the code i wrote to generate probability distribtuion of two random variable. now i would like to plot JPD.
clear all;
clc;
x1 = randn(1000,1);
x2 = 10*randn(1000,1);
[count_1, b] = hist(x1, 25); %25 bins
pd1 = count_1 / length(x1) / (b(2) - b(1)); % probability distribution function of x1
[count_2, bn] = hist(x2, 25); %25 bins
pd2 = count_2 / length(x2) / (bn(2) - bn(1)); % probabitlity distribtuion function of x2
%subplot(2,2,1), plot(x,s1)
%subplot(2,2,2),plot(x,s2)
%subplot(2,2,1),plot(b,pd1)
%subplot(2,2,2),plot(bn,pd2)
I am trying hard to get ans..plz any help out there..i have been tryihng over a month
Thanks..

Answer 1

I understand you don't have close form for your joint pdf, but "only the data". Using Matlab, you can indeed use this tool named hist3
% Generate random data
nData = 1e5;
data = zeros(2,nData);
m1 = 0; m2 = 1;
s1 = 1; s2 = 2;
for i=1:nData
d1 = m1+s1*randn;
d2 = m2+s2*randn;
data(:,i) = [d1; d2];
end
% hist3 will bin the data
xi = linspace(min(data(1,:)), max(data(1,:)), 50);
yi = linspace(min(data(2,:)), max(data(2,:)), 50);
hst = hist3(data,{xi yi}); %removed extra '
% normalize the histogram data
dx = xi(2)-xi(1);
dy = yi(2)-yi(1);
area = dx*dy;
pdfData = hst/sum(sum(hst))/area;
% plot pdf
figure(2); clf
contour(xi,yi,pdfData);
Hope this is of any help.