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

[Jean Sun]

Thanks a lot.
It does work. The fitted data match the simulated ones well. Even no need the shifted or scaled version of Chi-squared pdf. Also, I have tested the case of non-independent RVs,generated by linear combining of independent Gaussian RVs,the result is satisfactory too.

Regards,
J.Sun
	

2003-09-23 07:07:00 Thomas Lumley wrote£º

>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