linearJinhom {spatstat.linnet} | R Documentation |
Inhomogeneous Linear J-function for Point Processes on Linear Networks
Description
Computes an estimate of the inhomogeneous linear J
-function
for a point pattern on a linear network.
Usage
linearJinhom(X, lambda = NULL, lmin=NULL,
...,
r=NULL, rmax=NULL,
distance=c("path","euclidean"),
densitymethod=c("kernel", "Voronoi"),
sigma=bw.scott.iso,
f=0.2, nrep=200, ngrid=256)
Arguments
X |
Point pattern on linear network (object of class |
lambda |
Intensity values for the point pattern. Either a numeric vector,
a |
lmin |
Optional. The minimum possible value of the intensity over the network. A positive numerical value. |
r |
Optional. Numeric vector of values of the function argument |
rmax |
Optional. Numeric value specifying the largest desired value of |
distance |
A string (partially matched) specifying the
metric that will be used to measure distances between
points on the network: |
densitymethod |
String (partially matched) specifying the method that will be used to
estimate the intensity |
sigma |
Smoothing bandwidth used to estimate |
f , nrep |
Arguments passed to the algorithm for estimating the intensity
by Voronoi estimation, if |
... |
Additional arguments passed to the algorithms that estimate
the intensity, if |
ngrid |
Integer specifying the number of sample points on the network that
will be used to estimate the inhomogeneous empty space function
|
Details
This function computes the geometrically corrected inhomogeneous
linear J
-function for point processes on linear networks
defined by Cronie et al (2020).
The argument lambda
is the (estimated) intensity of the
underlying point process. It should be either a numeric vector
(giving intensity values at the points of X
),
a function
, a pixel image
(object of class "im"
or "linim"
) or
a fitted point process model (object of class "ppm"
or "lppm"
).
If lambda
is not given, it will be estimated from the observed
point pattern X
as follows:
If
densitymethod="kernel"
, the intensity will be estimated by kernel smoothing, using the fast estimatordensityQuick.lpp
introduced by Rakshit et al (2019). The smoothing bandwidthsigma
is required. It may be specified as a numeric value, or as a function that can be applied toX
to obtain a bandwidth value. Examples of the latter includebw.scott.iso
andbw.lppl
. Additional arguments...
will be passed tosigma
and todensityQuick.lpp
.If
densitymethod = "Voronoi"
, the intensity will be estimated using the resample-smoothed Voronoi estimatordensityVoronoi.lpp
introduced by Moradi et al (2019). The argumentsf
andnrep
are passed todensityVoronoi.lpp
and determine the retention probability and the number of replicates, respectively. Additional arguments...
will be passed todensityVoronoi.lpp
.
Value
Function value table (object of class "fv"
).
Author(s)
Mehdi Moradi m2.moradi@yahoo.com and Adrian Baddeley Adrian.Baddeley@curtin.edu.au.
References
Cronie, O., Moradi, M., and Mateu, J. (2020) Inhomogeneous higher-order summary statistics for point processes on linear networks. Statistics and Computing 30 (6) 1221–1239.
Moradi, M., Cronie, 0., Rubak, E., Lachieze-Rey, R., Mateu, J. and Baddeley, A. (2019) Resample-smoothing of Voronoi intensity estimators. Statistics and Computing 29 (5) 995–1010.
Rakshit, S., Davies, T., Moradi, M., McSwiggan, G., Nair, G., Mateu, J. and Baddeley, A. (2019) Fast kernel smoothing of point patterns on a large network using 2D convolution. International Statistical Review 87 (3) 531–556. DOI: 10.1111/insr.12327.
See Also
bw.scott.iso
,
bw.lppl
,
densityVoronoi.lpp
,
densityQuick.lpp
Examples
if(interactive()) {
plot(linearJinhom(spiders))
} else {
bottomhalf <- owin(c(0, 1125), c(0, 500))
plot(linearJinhom(spiders[bottomhalf]))
}