Inhomogeneous anisotropic pcf function, cylinder version — pcf_anin

Estimate a cylinder-pcf function for second order reweighted ("inhomogeneous") pattern.

Usage

pcf_anin_cylinder(
  x,
  u,
  epsilon,
  r,
  lambda = NULL,
  lambda_h,
  r_h,
  stoyan = 0.15,
  renormalise = TRUE,
  border = 1,
  aspect = 1/3,
  ...
)

Arguments

x: pp, list with $x~coordinates $bbox~bounding box
u: unit vector(s) of direction, as row vectors. Default: x and y axis.
epsilon: The cylinder half-width
r: radius vector at which to evaluate the function
lambda: optional vector of intensity estimates at points
lambda_h: if lambda missing, use this bandwidth in a kernel estimate of lambda(x)
r_h: smoothing for range dimension, epanechnikov kernel
stoyan: If r_h not given, use r_h=stoyan/lambda^(1/dim). Same as 'stoyan' in spatstat's pcf.
renormalise: See details.
border: Use translation correction? Default=1, yes. Only for cuboidal windows.
aspect: If given, instead of using a fixed halfwidth (epsilon) take the halfwidth to be r/(2*aspect). Default : 1/3
...: passed on to e.g. intensity_at_points

Value

Returns a dataframe.

Details

Computes a second order reweighted version of the cylinder-pcf, defined as the function to integrate in range over [0,R] to get the cylinder-K(R) function.

Lambda(x) at points can be given, or else it will be estimated using Epanechnikov kernel smoothing. See

If 'renormalise=TRUE', we normalise the lambda estimate so that sum(1/lambda(x))=|W|. This corresponds in spatstat's Kinhom to setting 'normpower=2'.