rMatClust.sphwin: Simulate the analogue of the Matern Cluster Process on the...

In baddstats/spherstat: Spatial Point Pattern Analysis, Geometry and Trigonometry for the Sphere

Simulate the analogue of the Matern Cluster Process on the sphere

Description

Generate a random point pattern, a simulated realisation of the analogue of the Matern Cluster Process on the sphere.

Usage

  rMatClust.sphwin(kappa, scale, mu, win=sphwin(type="sphere"), parents=FALSE,
 nsim=1, drop=TRUE, expand=TRUE, as.sp=TRUE, ndim="2")

Arguments

kappa	Intensity of the Poisson process of cluster centres. A single positive number.
scale	Radius parameter of the clusters.
mu	Mean number of points per cluster (a single positive number)
win	Window in which to simulate the pattern. An object of class sphwin.
parents	Logical. If TRUE, the parent points are included in the output, if FALSE parents are not included.
nsim	Number of simulated realisations to be generated.
drop	Logical. If nsim=1 and drop=TRUE (the default), the result will be a point pattern, rather than a list containing a point pattern.
expand	Logical. If TRUE (the default), the process is simulated on the entire sphere, and the output is only those points in the window defined by win. If FALSE, the process is simulated within the window defined by win.
as.sp	Logical. If TRUE, returns an object of class as defined by sp.dim. Otherwise, returns a matrix. See Value.
ndim	A string, taking value "2" or "3". Specifies whether the object should contain the locations of the points in spherical coordinates (ndim="2") or Cartesian coordinates (ndim="3").

Details

This algorithm generates a realisation of the analogue on the sphere of Matern's cluster process, a special case of the Neyman-Scott process, inside the window win.

This algorithm generates a uniform Poisson point process of “parent” points with intensity kappa. Then each parent point is replaced by a random cluster of “offspring” points, the number of points per cluster being Poisson (mu) distributed, and their positions being placed and uniformly inside a disc of radius r centred on the parent point. The resulting point pattern is a realisation of the classical “stationary Matern cluster process” generated inside the window win. This point process has intensity kappa * mu.

Value

If nsim=1 and drop=FALSE then a single item as described below; otherwise a list containing nsim items.

An item is determined by the values of as.sp and ndim:

If as.sp=FALSE and ndim="2", a two column matrix giving the locations of the simulated points.

If as.sp=FALSE and ndim="3", a three column matrix giving the locations of the simulated points.

If as.sp=TRUE and ndim="2", an object of class sp2 giving the locations of the simulated points.

If as.sp=TRUE and ndim="3", an object of class sp3 giving the locations of the simulated points.

Note

This function is the analogue for point processes on the sphere of the function rMatClust in spatstat, which is the corresponding function for point processes in R^2. Hence elements of this help page have been taken from that for spatstat with the permission of A. J. Baddeley. This enables the information on this help page to be consistent with that for rMatClust. It is hoped that this will minimise or remove any confusion for users of both spatstat and spherstat.

Author(s)

Tom Lawrence <email:[e-mail]> and Adrian Baddeley

References

Lawrence, T.J. (2017) Master's Thesis, University of Western Australia.

Matern, B. (1960) Spatial Variation. Meddelanden fraan Statens Skogsforskningsinstitut, volume 59, number 5. Statens Skogsforskningsinstitut, Sweden.

Matern, B. (1986) Spatial Variation. Lecture Notes in Statistics 36, Springer-Verlag, New York.

Waagepetersen, R. (2007) An estimating function approach to inference for inhomogeneous Neyman-Scott processes. Biometrics 63, 252–258.

See Also

rHardcore.sphwin, rMatClust, rMaternI.sphwin, rMaternII.sphwin, rpoispp.sphwin, rStrauss.sphwin, rThomas.sphwin

Examples

rM1 <- rMatClust.sphwin(250, 0.04*pi, 5, win=sphwin(), parents=FALSE)
rM1

baddstats/spherstat documentation built on Feb. 6, 2023, 1:45 a.m.