# gaussian in polar coordinates

• Apr 8th 2011, 09:02 PM
appsmail12
gaussian in polar coordinates
Hi everyone,

i'm trying to express an 3-D gaussian distribution into spherical coordinates as part of a schoolwork. First of all, is there really any benefit in doing this? It is not obvious to me. Does it help in calculating the density estimate, etc.?

Here is the gaussian function of N-Dimensions in cartesian coordinates:
$
N(\vec{x}|\vec\mu, \Sigma) =
\frac{1}{{(2 \pi)}^{D/2} }
\frac{1}{| \Sigma | ^{1/2}}
e ^ {- \frac{1}{2} (\vec{x}-\vec\mu)^T\Sigma^{-1}(\vec{x}-\vec\mu) }
$

And I have to use spherical coordinates for 3-D gaussian:

$x_1 = r cos \phi sin \theta$
$x_2 = r sin \phi sin \theta$
$x_3 = r cos \theta$