Given an observed pattern of points,
computes the Ripley-Rasson estimate of
the spatial domain from which they came.
Usage
ripras(x, y=NULL)
Arguments
x
vector of x coordinates of observed points,
or a 2-column matrix giving x,y coordinates,
or a list with components x,y giving coordinates.
y
(optional) vector of y coordinates of observed points,
if x is a vector.
Value
A window (an object of class "owin").
Details
Given an observed pattern of points with coordinates
given by x and y, this function computes
an estimate due to Ripley and Rasson (1977) of the
spatial domain from which the points came.
The points are
assumed to have been generated independently and uniformly
distributed inside an unknown domain $D$. The maximum
likelihood estimate of $D$ is the convex hull of the
points. Analogously to the problems of estimating the endpoint
of a uniform distribution, the MLE is not optimal.
Ripley and Rasson's estimator is a rescaled copy of the convex hull,
centred at the centroid of the convex hull.
The scaling factor is
$1/sqrt(1 - m/n)$
where $n$ is the number of data points and
$m$ the number of vertices of the convex hull.
References
Ripley, B.D. and Rasson, J.-P. (1977)
Finding the edge of a Poisson forest.
Journal of Applied Probability,
14, 483 -- 491.