# I want to estimate bivariate normal distribution and having trouble estimating it. How can i make it possible?

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VIJENDRA on 10 Oct 2014
Commented: Image Analyst on 21 Jul 2022
i want to estimate nomal probability density function of 2 variables (i.e. bivariate normal distribution ). i used this formula from Wikipedia:
my variables 'x' and 'y' are:
I write this code:
Covariance_matrix = cov(x,y); % estimated ro,sigma1 and sigma2 using this
ro = -0.0717;
mu1 = 0.1068;
mu2 = 0.8556;
sigma1 = 1.3250e-04;
sigma2 = 9.1330e-04;
sd1 = 0.0115;
sd2 = 0.0302;
Pdf = 1/(2*pi*sd1*sd2*sqrt(1-(ro^2))) * exp(-1/2*(1-ro^2)) * ((((x-mu1)/sigma1).^2) + (((y-mu2)/sigma2).^2)) - (2*ro*((x-mu1)*(y-mu2)/sd1*sd2));
My result is:
first of all i want to know am i going write and my second question is that i learnt probability ranges between 0 and 1 but in this case probability density values are very high so how is it possible? Please help.

Image Analyst on 10 Oct 2014
You tried to do too much in one line and messed up the parentheses. Split it apart into separate terms so that doesn't happen:
clc; % Clear the command window.
close all; % Close all figures (except those of imtool.)
imtool close all; % Close all imtool figures.
clear; % Erase all existing variables.
workspace; % Make sure the workspace panel is showing.
fontSize = 20;
format compact;
xl = linspace(-2, 2, 30);
yl = linspace(-2, 2, 30);
[x,y] = meshgrid(xl,yl);
Covariance_matrix = cov(x,y) % estimated ro,sigma1 and sigma2 using this
rho = -0.0717;
mu1 = 0.1068;
mu2 = 0.8556;
sigmaX = .51;
sigmaY = .91;
amplitude = 1 / (2 * pi* sigmaX * sigmaY * sqrt(1-rho^2))
factor = -1 / (2 * (1-rho^2))
term1 = ((x - mu1) / sigmaX) .^ 2;
term2 = ((y - mu2) / sigmaY) .^ 2;
term3 = 2 * rho * (x-mu1) * (y-mu2) / (sigmaX * sigmaY);
Pdf = amplitude * exp(factor * (term1 + term2 - term3));
surf(Pdf)
PRAKASH JOSHI on 21 Jul 2022
How do we change the angle of the bivariate gaussian, i m not able to change the angle of bivariate gaussian
Image Analyst on 21 Jul 2022
@PRAKASH JOSHI I'd probably take the result above and multiply it by a Rotation Matrix: