Bidimensional Gaussian Equation

[leomecma]

bidimensional gaussian

Anyone know the bidimensional gaussian equation (function of x mean, x variance, correlation x-y, y mean, y variance), I search it unsuccessful.


thks
leomecma

 

[claudiocamera]

bidimensional gaussian distribution

The papoulis book which is available in this forum deals a lot with this function.

You can dowload it and get more information, anyway the function is:

f(x,y) = A * exp [ B*C] where,

A = 1/ 2πσxσy√(1-r^2)

B= - 1/ 2(1-r^2)

C= [(x-ηx)/σx]^2 - 2r[(x-ηx)(y-ηy)/σxσy] + [(y-ηy)/σy]^2

ηx= mean of x
ηy=mean of y
σx= Standard deviation of x
σy= Standard deviation of y
r = Correlation coeficient = σxy/σxσy
σxy= Covariance of X and Y