Re: ci on radius

vontressms@xxxxxx wrote:
Ray Koopman wrote:
[...]
Would a true r of zero be equivalent to the true centroid of the (x,y)
distribution being at the origin?

yes. It would mean that all of the data would be centered close to the
origin. Hotteling's T^2 may be an equivalent test that r=0. I still
need a CI on r though.
Thanks.

Let n = the sample size,
m = the sample mean vector of (x,y),
S = the sample covariance matrix of (x,y),
u = the unknown true mean vector of (x,y).
Then the 100c% confidence region for u is
(u - m)' S^-1 (u - m) < F[2,n-2,c]*2(n-1)/(n(n-2)), where
F[a,b,c] = the c'th quantile of the F-distribution with df = (a,b).
The extrema of this ellipse can be taken as bounding r.

.