stdcpp | R Documentation |
Generate a realisation of the double-cluster process in a region S x T.
stdcpp(lambp, a, b, c, mu, s.region, t.region)
s.region |
Two-column matrix specifying polygonal region containing
all data locations.If |
t.region |
Vector containing the minimum and maximum values of the time interval. If |
lambp |
Intensity of the parent process. Can be either a numeric value, a function, or a 3d-array (see |
a |
Length of the semi-axes x of ellipsoid. |
b |
Length of the semi-axes y of ellipsoid. |
c |
Length of the semi-axes y of ellipsoid. |
mu |
Average number of daughter per parent. (a single positive number). |
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} x μ.
The simulated spatio-temporal point pattern.
Francisco J. Rodriguez Cortes <frrodriguezc@unal.edu.co>
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.
# Ellipsoid Xe <- stdcpp(lambp=20,a=0.5,b=0.09,c=0.07,mu=100) plot(Xe$xyt) # Spatio-temporal 3D scatter plot par(mfrow=c(1,1)) plot(Xe$xyt,type="scatter") # Balls Xb <- stdcpp(lambp=20,a=0.07,b=0.07,c=0.07,mu=100) plot(Xb$xyt) # Spatio-temporal 3D scatter plot par(mfrow=c(1,1)) plot(Xb$xyt,type="mark",style="elegant") # 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$xyt,s.region=Northcumbria, cex=0.5) # Spatio-temporal 3D scatter plot par(mfrow=c(1,1)) plot(X$xyt,type="scatter",theta=45,phi=30,cex=0.1, ticktype="detailed",col="black",style="elegant")
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