[R] Ellipse that Contains 95% of the Observed Data

[Barry Rowlingson]

On Mon, Mar 29, 2010 at 4:02 AM, Ben Bolker <bolker at ufl.edu> wrote:

>  I'll be interested to hear what others come up with.
>  I'm not sure the problem as you have stated it is well-posed, or
> necessarily possible. Suppose there is a true unknown
> bivariate probability distribution with a non-elliptical 95%
> quantile region. Will you be able to draw an ellipse that
> has the properties you want?

 I think the problem as posed doesn't produce a unique ellipse. You
could start with a circle of radius 0 centered on mean(x),mean(y) and
then increase the radius until it has 95% of the points in it. As long
as your points are in continuous space and with no coincident points
then you could do a simple bisection search on the radius.

 Similarly you could start with an ellipse of any eccentricity
centered at the same point with fixed angle and do the same. And the
ellipse doesn't even need to be centered at the mean point - it could
be waaay over to the left and eventually as it gets bigger it will
gobble up 95% of the points.

 Obviously with bivariate normally-distributed points we tend to show
the ellipse that is numerically derived from the mean and correlation
of the two normals, but that's not the only ellipse that takes 95% of
the points.

 So ummm I'm not sure what you should do. What is the question you are
trying to answer?

Barry