Estimate window from points alone
Given an observed pattern of points, computes the Ripley-Rasson estimate of the spatial domain from which they came.
- vector of
xcoordinates of observed points, or a 2-column matrix giving
x,ycoordinates, or a list with components
- (optional) vector of
ycoordinates of observed points, if
xis a vector.
Given an observed pattern of points with coordinates
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.
- A window (an object of class
Ripley, B.D. and Rasson, J.-P. (1977) Finding the edge of a Poisson forest. Journal of Applied Probability, 14, 483 -- 491.
plot(owin()) x <- runif(30) y <- runif(30) points(x,y) w <- ripras(x,y) plot(w, box=FALSE) points(x,y)