Re: Difference of two non central chi square distributions

From: David Jones (dajxxx_at_ceh.ac.uk)
Date: 06/24/04 

Date: Thu, 24 Jun 2004 17:40:56 +0100

Jose Angel wrote:
> Can anyone help me?
>
> I need to calculate the distribution of the difference of two
> non-central chi square variables. The sum is another chi-square
> distribution whose non-centrality parameter is the sum of the
> non-centrality parameters of each of the variables. But what about
> with the difference??And for the special case X-Y where X is
> non-central and Y central?
> Does anyone know?
>
> Thanks

Suggest you see:
Davies RB (1980) Alogorithm AS155 The Distribution of a linear
combination of (chi-squared) random variables. Applied Statistics,
29(3), 323-333

The Algortithm is in Algol. The cases covered include combinations of
non-central chi-squared with aribtrary (possibly negative)
coefficients, and allows also the addition of an extra Normal rv.

David Jones