rpp | R Documentation |
Generate one (or several) realisation(s) of the (homogeneous or inhomogeneous) Poisson process in a region S x T.
rpp(lambda, s.region, t.region, npoints=NULL, nsim=1, replace=TRUE, discrete.time=FALSE, nx=100, ny=100, nt=100, lmax=NULL, ...)
lambda |
Spatio-temporal intensity of the Poisson process.
If |
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 |
replace |
Logical allowing times repeat (should only be used when |
npoints |
Number of points to simulate. If |
discrete.time |
If TRUE, times belong to N, otherwise belong to R^+. |
nsim |
Number of simulations to generate. Default is 1. |
nx,ny,nt |
Define the size of the 3-D grid on which the intensity is evaluated. |
lmax |
Upper bound for the value of lambda(x,y,t), if
|
... |
Additional parameters if |
A list containing:
xyt |
Matrix (or list of matrices if |
Lambda |
nx x ny x nt array of the intensity surface at each time. |
s.region, t.region, lambda |
parameters passed in argument. |
Edith Gabriel <edith.gabriel@inrae.fr> and Peter J Diggle.
plot.stpp
, animation
and stan
for plotting space-time point patterns.
# Homogeneous Poisson process # --------------------------- hpp1 <- rpp(lambda=200,replace=FALSE) stan(hpp1$xyt) # fixed number of points, discrete time, with time repeat. data(northcumbria) hpp2 <- rpp(npoints=500, s.region=northcumbria, t.region=c(1,1000), discrete.time=TRUE) plot(hpp2$xyt, style="elegant") polymap(northcumbria) animation(hpp2$xyt, s.region=hpp2$s.region, t.region=hpp2$t.region, runtime=10, add=TRUE) # Inhomogeneous Poisson process # ----------------------------- # intensity defined by a function lbda1 = function(x,y,t,a){a*exp(-4*y) * exp(-2*t)} ipp1 = rpp(lambda=lbda1, npoints=400, a=3200/((1-exp(-4))*(1-exp(-2)))) stan(ipp1$xyt) # intensity defined by a matrix data(fmd) data(northcumbria) h = mse2d(as.points(fmd[,1:2]), northcumbria, nsmse=30, range=3000) h = h$h[which.min(h$mse)] Ls = kernel2d(as.points(fmd[,1:2]), northcumbria, h, nx=100, ny=100) Lt = dim(fmd)[1]*density(fmd[,3], n=200)$y Lst=array(0,dim=c(100,100,200)) for(k in 1:200) Lst[,,k] <- Ls$z*Lt[k]/dim(fmd)[1] ipp2 = rpp(lambda=Lst, s.region=northcumbria, t.region=c(1,200), discrete.time=TRUE) par(mfrow=c(1,1)) image(Ls$x, Ls$y, Ls$z, col=grey((1000:1)/1000)); polygon(northcumbria) animation(ipp2$xyt, add=TRUE, cex=0.5, runtime=15)
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