# Thread: How is the sum of inverse squares distributed?

1. ## How is the sum of inverse squares distributed?

if ${r_i}, {i=1..N}$ is normally distributed with equal mean and variance, how is the sum of N inverse squares

$\sum_{i=1}^{N}\frac{1}{{r_i}^2}$

distributed?

2. Ok, so for r ~ N(0,1) i can model the distribution as the convolution of the inverse chi squared pdfs.

Now, who can tell me how to do it for non-centrally distributed terms (i.e. $\frac{1}{(r-r_0)^2}$) ? Is there an expression for a noncentral inverse chi squared distribution?