sim.poissonc {ecespa} | 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
ppp format of spatstat. |
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, accordingto 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) = (2*pi*sigma^2)^-1 exp{-(x^2+y^2)/2*sigma^2}
The simulated point pattern (an object of class "ppp
").
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 marcelino.delacruz@upm.es
Diggle, P.J. 2003. Statistical analysis of spatial point patterns. Arnold, London.
rNeymanScott
in spatstat
## Not run: require(spatstat) data(gypsophylous) ## Estimate K function ("Kobs"). gyps.env <- envelope(gypsophylous, Kest, correction="iso") plot(gyps.env, sqrt(./pi)-r~r) ## 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$r, lty=2, lwd=3, col="purple") ## A kind of pointwise test of the pattern gypsophilous been a realisation ## of the fitted model, simulating with sim.poissonc and using function J (Jest). gyps.env.sim = envelope(gypsophylous, Jest, simulate=expression(sim.poissonc(gypsophylous, sigma=sqrt(cosa.pc$sigma2), rho=cosa.pc$rho))) plot(gyps.env.sim, main="") ## End(Not run)