stdcpp: Spatio-temporal double 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	stdcpp(lambp, a, b, c, mu, s.region, t.region)

`lambp`	Intensity of the Poisson process of cluster centres. A single positive number or function.
`a`	Length of the semi-axes x of ellipsoid.
`b`	Length of the semi-axes y of ellipsoid.
`c`	Length of the semi-axes z of ellipsoid.
`mu`	Mean number of points per cluster (a single positive number).
`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.

We consider the straightforward extension of the classical Matern cluster process on the R^3 case (with ellipsoid or balls) by considering the z-coordiantes as times.

Consider a Poisson point process in the plane with intensity λ_{p} as cluster centres for all times 'parent', as well as a ellipsoid (or ball) where the semi-axes are of lengths a, b and c, around of each Poisson point under a random general rotation. The scatter uniformly in all ellipsoid (or ball) 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)

# Ellipsoid
Xe <- stdcpp(lambp=20, a=0.12, b=0.09, c=0.07, mu=100)
plot(Xe$xyt)

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

# Balls
Xb <- stdcpp(lambp=20, a=0.05, b=0.05, c=0.05, mu=100)
plot(Xb$xyt)

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

# Northcumbria
data(northcumbria)
Northcumbria <- northcumbria/1000
X <- stdcpp(lambp=0.00004, a=10,b=10,c=10, mu=120, s.region=Northcumbria, t.region=c(0,200))
plot(X$xyt,s.region=Northcumbria)

# plot scatterplot3d
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")

## End(Not run)