This is a relatively recent article that is somewhat accessible. Jensen, D. R., and Solomon, Herbert (1994), "Approximations to joint distributions of definite quadratic forms", Journal of the American Statistical Association, 89 , 480-486 It has references to previous work.
I also have an old paper that is so old I can't tell what journal it came out of:( Grad, Arthur and Solomon, Herbert "Distribution of Quadratic Forms and Some Applications" probably published in 55 or 56 but I can't tell. The paper by Grad and Solomon uses the moment generating function to give the exact distribution and various approximations to produce a table for a sum of 2 or 3 variates. Usual disclaimers ... Bob -----Original Message----- From: Thomas Lumley [mailto:[EMAIL PROTECTED] Sent: Tuesday, September 23, 2003 10:07 AM To: Jean Sun Cc: [EMAIL PROTECTED] Subject: Re: [R] what does the sum of square of Gaussian RVs with different variance obey? 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 ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help [[alternative HTML version deleted]] ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help
