Jinhom(X, lambda = NULL, lmin = NULL, ..., sigma = NULL, varcov = NULL, r = NULL, breaks = NULL, update = TRUE)"ppp"
or in a format recognised by as.ppp()
X,
a pixel image (object of class "im") giving the
intensity values at all locations, a fitted point process model
(object of class "ppm" or "kppm") or a function(x,y) which
can be evaluated to give the intensity value at any location.
density.ppp
to control the smoothing bandwidth, when lambda is
estimated by kernel smoothing.
as.mask to control
the pixel resolution, or passed to density.ppp
to control the smoothing bandwidth.
lambda is a fitted model
(class "ppm" or "kppm")
and update=TRUE (the default),
the model will first be refitted to the data X
(using update.ppm or update.kppm)
before the fitted intensity is computed.
If update=FALSE, the fitted intensity of the
model will be computed without fitting it to X.
Jest. The argument X should be a point pattern
(object of class "ppp").
The inhomogeneous $J$ function is computed as
$Jinhom(r) = (1 - Ginhom(r))/(1-Finhom(r))$
where $Ginhom, Finhom$ are the inhomogeneous $G$ and $F$
functions computed using the border correction
(equations (7) and (6) respectively in Van Lieshout, 2010).
The argument lambda should supply the
(estimated) values of the intensity function $lambda$
of the point process. It may be either
If lambda is a numeric vector, then its length should
be equal to the number of points in the pattern X.
The value lambda[i] is assumed to be the
the (estimated) value of the intensity
$lambda(x[i])$ for
the point $x[i]$ of the pattern $X$.
Each value must be a positive number; NA's are not allowed.
If lambda is a pixel image, the domain of the image should
cover the entire window of the point pattern. If it does not (which
may occur near the boundary because of discretisation error),
then the missing pixel values
will be obtained by applying a Gaussian blur to lambda using
blur, then looking up the values of this blurred image
for the missing locations.
(A warning will be issued in this case.)
If lambda is a function, then it will be evaluated in the
form lambda(x,y) where x and y are vectors
of coordinates of the points of X. It should return a numeric
vector with length equal to the number of points in X.
If lambda is omitted, then it will be estimated using
a `leave-one-out' kernel smoother,
as described in Baddeley, Moller
and Waagepetersen (2000). The estimate lambda[i] for the
point X[i] is computed by removing X[i] from the
point pattern, applying kernel smoothing to the remaining points using
density.ppp, and evaluating the smoothed intensity
at the point X[i]. The smoothing kernel bandwidth is controlled
by the arguments sigma and varcov, which are passed to
density.ppp along with any extra arguments.
van Lieshout, M.N.M. and Baddeley, A.J. (1996) A nonparametric measure of spatial interaction in point patterns. Statistica Neerlandica 50, 344--361.
van Lieshout, M.N.M. (2010) A J-function for inhomogeneous point processes. Statistica Neerlandica 65, 183--201.
Ginhom,
Finhom,
Jest
## Not run:
# plot(Jinhom(swedishpines, sigma=bw.diggle, adjust=2))
# ## End(Not run)
plot(Jinhom(swedishpines, sigma=10))
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