NScluster (version 1.1.0)

PalmIP: Non-Parametric Estimate of The Palm Intensity of The Inverse-Power Type

Description

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

Usage

PalmIP(offspring, pa, delta, ty, x2, plot=TRUE)

Arguments

offspring

the list of coordinates $(x,y)$ of offspring points.

pa

the parameters $(mu_i, nu_i, p_i, c_i)$, $i=1,2,...,I

delta

a width for the non-parametric Palm intensity function.

ty

the variable $Ty$ for the standardized coordinates of points in the rectangular region $[0,1]*[0,Ty]$ without loss of generality except for the scaling.

x2

upper limit value in place of $infty$.

plot

logical. If TRUE (default) the non-parametric estimate and the curves of the true and MPLE (the maximum Palm likelihood estimator) parameters are shown.

Value

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

  ## simulation
  seeds <- c(822, 913, 905)
  pa1 <- c(50, 30, 1.5, 0.005)
  ty <- 1
  z <- SimulateIP(seeds, pa1, ty) 

  ## estimation
  delta <- 0.001
  x2 <- 0.3
  pa2 <- c(0.5651715e+02, 0.2392856e+02, 0.1600531e+01, 0.5565606e-02)
  pa <- matrix(c(pa1,pa2), 2, 4, byrow=TRUE) 
  PalmIP(z$offspring, pa, delta, ty, x2)