Estimate window from points alone
Given an observed pattern of points, computes the Ripley-Rasson estimate of the spatial domain from which they came.
ripras(x, y=NULL, shape="convex")
- vector of
xcoordinates of observed points, or a 2-column matrix giving
x,ycoordinates, or a list with components
x,ygiving coordinates (such as a point pattern object of class
- (optional) vector of
ycoordinates of observed points, if
xis a vector.
- String indicating the type of window to be estimated:
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 $D$.
shape="convex" (the default), the domain $D$ is assumed
to be a convex set. The maximum
likelihood estimate of $D$ is the convex hull of the
points (computed by
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.
shape="rectangle", the domain $D$ is assumed
to be a rectangle with sides parallel to the coordinate axes. The maximum
likelihood estimate of $D$ is the bounding box of the points
bounding.box.xy). The Ripley-Rasson
estimator is a rescaled copy of the bounding box,
with scaling factor $1/sqrt(1 - 4/n)$
where $n$ is the number of data points,
centred at the centroid of the bounding box.
- 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.
x <- runif(30) y <- runif(30) w <- ripras(x,y) plot(owin(), main="ripras(x,y)") plot(w, add=TRUE) points(x,y) X <- rpoispp(15) plot(X, main="ripras(X)") plot(ripras(X), add=TRUE)