sim.poissonc | R Documentation |
Generate a random point pattern, a simulated realisation of the Poisson Cluster Process
sim.poissonc(x.ppp, rho, sigma)
x.ppp |
Point pattern whose window and intensity will be simulated. An object with the
|
rho |
Parameter rho of the Poisson Cluster process. |
sigma |
Parameter sigma of the Poisson Cluster process. |
The Poisson cluster processes are defined by the following postulates (Diggle 2003):
PCP1 | Parent events form a Poisson process with intensity rho. |
PCP2 | Each parent produces a random number of offspring, according to a probability distribution |
p[s]: s = 0, 1, 2, ... | |
PCP3 | The positions of the offspring relative to their parents are distributed according to a bivariate pdf h. |
This implementation asumes that the probability distribution p[s] of offspring per parent is a Poisson distribution and that the position of each offspring relative to its parent follows a radially symetric Gaussian distribution with pdf
h(x, y) = [1/(2*pi*sigma^2)]* exp[-(x^2+y^2)/(2*sigma^2)]
The simulated point pattern (an object of class "ppp
").
This implementation simulates only point patterns within rectangular windows. Use ipc.estK
to fit and
rIPCP
(or the spatstat
functions) to simulate point patterns within irregular windows.
This function can use the results of pc.estK
to simulate point patterns from a fitted model.
Be careful as the paramted returned by pc.estK
is sigma^2 while sim.poissonc
takes
its square root, i.e. sigma.
Marcelino de la Cruz Rot
Diggle, P.J. 2003. Statistical analysis of spatial point patterns. Arnold, London.
rIPCP
to simulate inhomogeneous PCP; rNeymanScott
and rThomas
in spatstat
data(gypsophylous) # set the number of simulations (nsim=199 or larger for real analyses) nsim<- 39 ## Estimate K function ("Kobs"). gyps.env <- envelope(gypsophylous, Kest, correction="iso", nsim=nsim) plot(gyps.env, sqrt(./pi)-r~r, legend=FALSE) ## Fit Poisson Cluster Process. The limits of integration ## rmin and rmax are setup to 0 and 60, respectively. cosa.pc <- pc.estK(Kobs = gyps.env$obs[gyps.env$r<=60], r = gyps.env$r[gyps.env$r<=60]) ## Add fitted Kclust function to the plot. lines(gyps.env$r,sqrt(Kclust(gyps.env$r, cosa.pc$sigma2,cosa.pc$rho)/pi)-gyps.env$r, lty=2, lwd=3, col="purple") ## A kind of pointwise test of the pattern gypsophilous been a realisation ## of the fitted model, simulating with sim.poissonc and using function J (Jest). gyps.env.sim <- envelope(gypsophylous, Jest, nsim=nsim, simulate=expression(sim.poissonc(gypsophylous, sigma=sqrt(cosa.pc$sigma2), rho=cosa.pc$rho))) plot(gyps.env.sim, main="")
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