[R] what does the sum of square of Gaussian RVs with different variance obey?

[Thomas Lumley]

On Tue, 23 Sep 2003, Jean Sun wrote:

> >From basic statistics principle,we know,given several i.i.d Gaussian
> >RVs with zero or nonzero mean,the sum of square of them is a central or
> >noncentral Chi-distributed RV.However if these Gaussian RVs have
> >different variances,what does the sum of square of them obey?
>

Nothing very useful.  It's a mixture of chisquare(1) variables. One
standard approach is to approximate it by a multiple of a chisquared
distribution that has the correct mean and variance.

	-thomas