sthpcpp: Spatio-temporal hot-spots cluster point process model
In frajaroco/mvstpp: Mark variogram for spatio-temporal point processes

Description Usage Arguments Details Value Author(s) References Examples

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

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

`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.

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 λ_{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 (μ) distribution. The resulting point pattern is a spatio-temporal cluster point process with t=z. This point process has intensity λ_{p} * μ.

The simulated spatio-temporal point pattern.

Francisco J. Rodriguez Cortes <cortesf@uji.es> https://fjrodriguezcortes.wordpress.com

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 Gille, W. (2017). Mark variograms for spatio-temporal point processes. Spatial Statistics. 20, 125-147.

## 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)