sthpcpp: Spatio-temporal hot-spots cluster point process model

In frajaroco/msfstpp: Mark summary functions for spatio-temporal point processes

Spatio-temporal hot-spots cluster point process model

Description

Generate a random spatio-temporal point pattern, a simulated realisation of the cluster process.

Usage

sthpcpp(lambp, r, mu, s.region, t.region)

Arguments

lambp	Intensity of the Poisson process of cluster centres.
r	Radius parameter of the clusters.
mu	Mean number of points per cluster (a single positive number) or reference intensity for the cluster points (a function or a pixel image).
s.region	A two-column matrix specifying a polygonal region containing all data locations. If s.region is missing, the Ripley-Rasson estimate convex spatial domain is considered.
t.region	A vector containing the minimum and maximum values of the time interval. If t.region is missing, the range of xyt[,3] is considered.

Details

This function generates a realisation of spatio-temporal cluster process, which can be considered as generalisation of the classical Matern cluster process, inside the spatio-temporal window.

Consider a Poisson point process in the plane with intensity \lambda_{p} as cluster centres for all times 'parent', as well as a infinite cylinder of radius R around of each Poisson point, orthogonal to the plane. The scatter uniformly in all cylinders of all points which are of the form (x,y,z), the number of points in each cluster being random with a Poisson (\mu) distribution. The resulting point pattern is a spatio-temporal cluster point process with t=z. This point process has intensity \lambda_{p} * \mu.

Value

The simulated spatio-temporal point pattern.

Author(s)

Francisco J. Rodriguez Cortes <[e-mail]> https://fjrodriguezcortes.wordpress.com

References

Baddeley, A., Rubak, E., Turner, R. (2015). Spatial Point Patterns: Methodology and Applications with R. CRC Press, Boca Raton.

Chiu, S. N., Stoyan, D., Kendall, W. S., and Mecke, J. (2013). Stochastic Geometry and its Applications. John Wiley & Sons.

Gabriel, E., Rowlingson, B., Diggle P J. (2013) stpp: an R package for plotting, simulating and analyzing Spatio-Temporal Point Patterns. Journal of Statistical Software 53, 1-29.

Illian, J B., Penttinen, A., Stoyan, H. and Stoyan, D. (2008). Statistical Analysis and Modelling of Spatial Point Patterns. John Wiley and Sons, London.

Stoyan, D., Rodriguez-Cortes, F. J., Mateu, J. and Wilfried, G. (2016). Mark variograms for spatio-temporal point processes, Submitted .

See Also

Rodriguez-Cortes, F. J.(2015). mvstpp: Mark Variogram for Spatio-Temporal Point Processes. GitHub repository. URL https://github.com/frajaroco/mvstpp.

Examples

## Not run:
#################
require(plot3D)

X <- sthpcpp(lambp=20, r=0.05, mu=100)
plot(X$xyt)

par(mfrow=c(1,1))
scatter3D(X$xyt[,1],X$xyt[,2],X$xyt[,3],theta=45,phi=30,
main="Spatio-temporal point pattern",xlab="\n x",ylab="\n y",
zlab="\n t",ticktype="detailed",col="black")

## Spatio-temporal hot-spots cluster point process model
data(northcumbria)
Northcumbria <- northcumbria/1000
Xo <- sthpcpp(lambp=0.0035, r=5, mu=200, s.region=Northcumbria, 
                   t.region=c(28,198))
plot(Xo$xyt,s.region=Northcumbria)

# plot scatterplot3d
par(mfrow=c(1,1))
scatter3D(Xo$xyt[,1],Xo$xyt[,2],Xo$xyt[,3],theta=45,phi=30,
main="Spatio-temporal point pattern",xlab="\n x",ylab="\n y",
zlab="\n t",ticktype="detailed",col="black")

## End(Not run)

frajaroco/msfstpp documentation built on July 24, 2024, 6:34 a.m.