# [R] R help

Rolf Turner rolf at math.unb.ca
Tue Apr 29 23:49:47 CEST 2003

```Peter Dalgaard writes:

> Shutnik <shutnik_xx at yahoo.co.uk> writes:
>
> >  Hello,
> >  I have the normal random variables y(t)~N(mu, sigma.sq) and want
> >  to decompose them into n normal variables:
> >
> >  y(t) = x(t,1) +
+ x(t,n)

I presume this means y(t) = x(t,1) + ... + x(t,n)  (R.T.)

> >
> > x(t,i)~N(mu, sigma.sq/n)

I presume you want x(t,i)~N(mu/n, sigma.sq/n),
elsewise the question doesn't make sense.

I also presume you want the x(t,i) to be independent,
elsewise the question is trivial.                  (R.T.)

> >
> >  The problem is not as simple as can appear. All my experiments
> >  didnt give me anything so far. Are there any tools to do this?
> >
>
> This should work, provided I understand the problem correctly:
>
> x <- rnorm(n,sd=sqrt(sigma.sq/n))
> x <- x - mean(x) + y/n

I don't think it's that simple:  By my calculations,

Var(x_i) = 2*sigma.sq/n - sigma.sq/n^2,  not sigma.sq/n.

I think the problem is actually fairly subtle (although I may
be overlooking something simple).  Something like a Gramm-Schmidt
approach should work, but I can't quite suss it out.

cheers,

Rolf Turner
rolf at math.unb.ca

```