Inhomogeneous Linear K Function
Computes an estimate of the inhomogeneous linear $K$ function for a point pattern on a linear network.
linearKinhom(X, lambda=NULL, r=NULL, ..., correction="Ang", normalise=TRUE)
- Point pattern on linear network (object of class
- Intensity values for the point pattern. Either a numeric vector,
function, a pixel image (object of class
"linim") or a fitted point process model (object of class
- Optional. Numeric vector of values of the function argument $r$. There is a sensible default.
- Geometry correction.
"Ang". See Details.
- Logical. If
TRUE(the default), the denominator of the estimator is data-dependent (equal to the sum of the reciprocal intensities at the data points), which reduces the sampling variability. If
FALSE, the denominato
This command computes the inhomogeneous version of the linear $K$ function from point pattern data on a linear network.
lambda = NULL the result is equivalent to the
homogeneous $K$ function
lambda is given, then it is expected to provide estimated values
of the intensity of the point process at each point of
lambda may be a numeric vector (of length equal to
the number of points in
X), or a
function(x,y) that will be
evaluated at the points of
X to yield numeric values,
or a pixel image (object of class
"im") or a fitted point
process model (object of class
lambda is a fitted point process model,
the default behaviour is to update the model by re-fitting it to
the data, before computing the fitted intensity.
This can be disabled by setting
correction="none", the calculations do not include
any correction for the geometry of the linear network.
correction="Ang", the pair counts are weighted using
Ang's correction (Ang, 2010).
- Function value table (object of class
Ang, Q.W. (2010) Statistical methodology for spatial point patterns on a linear network. MSc thesis, University of Western Australia. Ang, Q.W., Baddeley, A. and Nair, G. (2012) Geometrically corrected second-order analysis of events on a linear network, with applications to ecology and criminology. Scandinavian Journal of Statistics 39, 591--617.
data(simplenet) X <- rpoislpp(5, simplenet) fit <- lppm(X, ~x) K <- linearKinhom(X, lambda=fit) plot(K)