# PalmTypeB: 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 Type B model estimated directly from a set of point pattern data.

## Usage

 `1` ``` PalmTypeB(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 (`mu1`, `mu2`, `nu`, `sigma1`, `sigma2`), where (`mu`i, `nu`, `sigma`i) is an intensity of parents, an expected number of descendants, a parameter of the dispersal kernel for superposed component i (i = 1,2), respectively. `pars2` a named vector of MPLEs (the maximum Palm likelihood estimates) (`mu1`, `mu2`, `nu`, `sigma1`, `sigma2`). `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 `EstimateTypeB`.

## 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(mu1 = 10.0, mu2 = 40.0, nu = 30.0, sigma1 = 0.01, sigma2 = 0.03) z <- SimulateTypeB(pars, seed = 257) ## estimation ## need very long c.p.u time in the minimization procedure ## Not run: init.pars <- c(mu1 = 20.0, mu2 = 30.0, nu = 30.0, sigma1 = 0.02, sigma2 = 0.02) z1 <- EstimateTypeB(z\$offspring\$xy, init.pars) # Parameter mu1 mu2 nu sigma1 sigma2 # Initial value 20.0000 30.0000 30.0000 0.0200 0.0200 # MPLE 16.1778 44.3974 28.3942 0.0101 0.0312 ## End(Not run) ## Palm intensity par1 <- c(10.0, 40.0, 30.0, 0.01, 0.03) # pars par2 <- c(16.1778, 44.3974, 28.3942, 0.0101, 0.0312) # z1\$mple PalmTypeB(z\$offspring\$xy, par1, par2) ```

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