# PalmIP: Non-Parametric and Parametric Estimate of the Palm Intensity... In NScluster: Simulation and Estimation of the Neyman-Scott Type Spatial Cluster Models

## 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

 ```1 2``` ``` 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```## 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.