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

Thomas Lumley tlumley at u.washington.edu
Tue Sep 23 16:07:09 CEST 2003

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.


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