Neyman-Scott cluster process: moments and simulation

Parents form a Poisson process of intensity kappa; each has a Poisson(mu) number of offspring displaced by the kernel: "thomas" (isotropic Gaussian, sd scale), "cauchy" (bivariate Cauchy with scale scale) or "matern" (uniform in a disc of radius scale). The intensity is \(\kappa\mu\); the K function and pair correlation are those of spatstat.random::spatstatClusterModelInfo. With simulate > 0 and a rectangular window the process is simulated with parents in the window dilated by the radius beyond which an offspring falls with probability 1e-3 (Thomas, Matern exact) or 1e-2 (Cauchy), from the same Philox streams as the Python arm.

Usage

NeymanScottProcess(
  kappa,
  mu,
  scale,
  kernel = c("thomas", "cauchy", "matern"),
  r = NULL,
  window = NULL,
  simulate = 0L,
  seed = 0
)

Arguments

kappa: Parent intensity.
mu: Mean number of offspring per parent.
scale: Kernel scale.
kernel: "thomas", "cauchy" or "matern".
r: Distances at which to evaluate K and g.
window: Rectangle c(xmin, xmax, ymin, ymax) for simulation.
simulate: Number of patterns to simulate.
seed: Philox key.

Value

List with intensity, K, pcf, r, simulated.

References

Neyman, J. and Scott, E. L. (1958). Statistical approach to problems of cosmology. Journal of the Royal Statistical Society B 20, 1-43.

Thomas, M. (1949). A generalization of Poisson's binomial limit for use in ecology. Biometrika 36, 18-25.

Ghorbani, M. (2013). Cauchy cluster process. Metrika 76, 697-706.

Examples

NeymanScottProcess(10, 5, 0.05, r = 0.1)$K
#> [1] 0.09462798