PalmIP: Non-Parametric and Parametric Estimate of the Palm Intensity...

Description Usage Arguments Value References Examples

View source: R/NScluster.R

Description

Calculate the non-parametric and parametric Palm intensity function of the Inverse-power type model estimated directly from a set of point pattern data.

Usage

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  PalmIP(xy.points, pars1 = NULL, pars2 = NULL, delta = 0.001, uplimit = 0.3,
         plot=TRUE)

Arguments

xy.points

a matrix containing the coordinates (x,y) of points in a unit square: W=[0,1]*[0,1].

pars1

a named vector of true parameters (mu, nu, p, c), where mu is an intensity of parents, nu is an expected number of descendants for each parent, p is the decay order and c is the scaling parameter.

pars2

a named vector of MPLEs (the maximum Palm likelihood estimates) (mu, nu, p, c).

delta

a width for the non-parametric Palm intensity function.

uplimit

upper limit value in place of .

plot

logical. If TRUE (default), the non-parametric estimate and the curves of true parameters and MPLEs are shown.

Value

r

the distance r=jΔ, where j=1,2,...,[R/Δ], where [ ] is the Gauss' symbol and R=1/2 is given in the program for the normalized rectangular region for the point pattern.

np.palm

the corresponding values of the non-parametric Palm intensity function of r, which is normalized by the total intensity estimate of the point pattern data.

palm.normal

the normalized Palm intensity functions λ_o(r)/λ^ calculated from the given sets of parameter values. See ../doc/NScluster-guide.pdf.

References

U. Tanaka, Y. Ogata and K. Katsura, Simulation and estimation of the Neyman-Scott type spatial cluster models, Computer Science Monographs No.34, 2008, 1-44. The Institute of Statistical Mathematics.

Examples

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## simulation
pars <- c(mu = 50.0, nu = 30.0, p = 1.5, c = 0.005)
z <- SimulateIP(pars, seed = 353)

## estimation
## need very long c.p.u time in the minimization procedure
## Not run: 
init.pars <- c(mu = 55.0, nu = 35.0, p = 1.0, c = 0.01)
z1 <- EstimateIP(z$offspring$xy, init.pars, skip = 100)
# Parameter               mu            nu             p             c
# Initial value      55.0000       35.0000        1.0000        0.0100
# MPLE               48.3143       30.5047        1.6467        0.0079

## End(Not run)

## Palm intensity
par1 <- c(50.0, 30.0, 1.5, 0.005)  # pars
par2 <- c(48.3143, 30.5047, 1.6467, 0.0079) # z1$mple
PalmIP(z$offspring$xy, par1, par2)

NScluster documentation built on March 19, 2018, 9:03 a.m.