palm.cppm {NScluster} | R Documentation |
Compute the non-parametric and the parametric Palm intensity function of the Neyman-Scott cluster point process models and their extensions.
palm.cppm(mple, pars = NULL, delta = 0.001, uplimit = 0.3) ## S3 method for class 'Palm' print(x, ...)
mple |
an object of class "mple". |
pars |
a named vector of the true parameters, if any. |
delta |
a width for the non-parametric Palm intensity function. |
uplimit |
upper limit in place of ∞ of the integral in the
probability distribution function relative to the random distance between
two descendant points within the same cluster. The |
x |
an object of class |
... |
ignored. |
An object of class "Palm"
containing the following components:
r |
the distance r=jΔ, where j=1,2,…,[R/Δ], [.] is the Gauss' symbol and R=1/2 in the program. |
np.palm |
the corresponding values of the non-parametric Palm intensity function, which is normalized by the total intensity estimate (the mean number of points in W) of a given point pattern data. |
norm.palm |
the corresponding values of the normalized Palm intensity
function, i.e.,
λ_o(r)/λ^, where λ_o(r) is the
Palm intensity and λ is an intensity of a cluster point process
model. See 'Details' in |
There is another method plot.Palm
for this class.
Tanaka, U., Ogata, Y. and Katsura, K. (2008) Simulation and estimation of the Neyman-Scott type spatial cluster models. Computer Science Monographs 34, 1-44. The Institute of Statistical Mathematics, Tokyo. https://www.ism.ac.jp/editsec/csm/.
See sim.cppm
and mple.cppm
to simulate the
Neyman-Scott cluster point process models and their extensions and to compute
the MPLEs, respectively.
## Not run: # The computation of MPLEs takes a long CPU time in the minimization procedure, # especially for the Inverse-power type and the Type A models. ### Thomas Model #simulation pars <- c(mu = 50.0, nu = 30.0, sigma = 0.03) t.sim <- sim.cppm("Thomas", pars, seed = 117) ## estimation => Palm intensity init.pars <- c(mu = 40.0, nu = 40.0, sigma = 0.05) t.mple <- mple.cppm("Thomas", t.sim$offspring$xy, init.pars) t.palm <- palm.cppm(t.mple, pars) plot(t.palm) ### Inverse-Power Type Model # simulation pars <- c(mu = 50.0, nu = 30.0, p = 1.5, c = 0.005) ip.sim <- sim.cppm("IP", pars, seed = 353) ## estimation => Palm intensity init.pars <- c(mu = 55.0, nu = 35.0, p = 1.0, c = 0.01) ip.mple <- mple.cppm("IP", ip.sim$offspring$xy, init.pars, skip = 100) ip.palm <- palm.cppm(ip.mple, pars) plot(ip.palm) ### Type A Model # simulation pars <- c(mu = 50.0, nu = 30.0, a = 0.3, sigma1 = 0.005, sigma2 = 0.1) a.sim <- sim.cppm("TypeA", pars, seed=575) ## estimation => Palm intensity init.pars <- c(mu=60.0, nu=40.0, a=0.5, sigma1=0.01, sigma2=0.1) a.mple <- mple.cppm("TypeA", a.sim$offspring$xy, init.pars, skip=100) a.palm <- palm.cppm(a.mple, pars) plot(a.palm) ### Type B Model # simulation pars <- c(mu1 = 10.0, mu2 = 40.0, nu = 30.0, sigma1 = 0.01, sigma2 = 0.03) b.sim <- sim.cppm("TypeB", pars, seed = 257) ## estimation => Palm intensity init.pars <- c(mu1 = 20.0, mu2 = 30.0, nu = 30.0, sigma1 = 0.02, sigma2 = 0.02) b.mple <- mple.cppm("TypeB", b.sim$offspring$xy, init.pars) b.palm <- palm.cppm(b.mple, pars) plot(b.palm) ### Type C Model # simulation pars <- c(mu1 = 5.0, mu2 = 9.0, nu1 = 30.0, nu2 = 150.0, sigma1 = 0.01, sigma2 = 0.05) c.sim <- sim.cppm("TypeC", pars, seed = 555) ## estimation => Palm intensity init.pars <- c(mu1 = 10.0, mu2 = 10.0, nu1 = 30.0, nu2 = 120.0, sigma1 = 0.03, sigma2 = 0.03) c.mple <- mple.cppm("TypeC", c.sim$offspring$xy, init.pars) c.palm <- palm.cppm(c.mple, pars) plot(c.palm) ## End(Not run)