PalmThomas: 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 Thomas model estimated directly from a set of point pattern data.

Usage

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  PalmThomas(xy.points, pars1 = NULL, pars2 = NULL, delta = 0.001, 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 the true parameters (mu, nu, sigma), where mu is an intensity of parents, nu is an expected number of descendants for each parent and sigma is a parameter of the dispersal kernel.

pars2

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

delta

a width for the non-parametric Palm intensity function.

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 'Details' in EstimateThomas.

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, sigma = 0.03)
z <- SimulateThomas(pars, seed = 117)

## estimation
## need long c.p.u time in the minimization procedure
## Not run: 
init.pars <- c(mu = 40.0, nu = 40.0, sigma = 0.05)
z1 <- EstimateThomas(z$offspring$xy, init.pars)
# Parameter               mu            nu         sigma
# Initial value      40.0000       40.0000        0.0500
# MPLE               46.7657       27.2079        0.0279

## End(Not run)


## Palm intensity
par1 <- c(50.0, 30.0, 0.03)  # pars
par2 <- c(46.7657, 27.2079, 0.0279)  # z1$mple
PalmThomas(z$offspring$xy, par1, par2)

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