R help - Sep 2003 - what does the sum of square of Gaussian RVs with different variance obey?

>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?
Thanks in advance.

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