Inhomogeneous anisotropic pcf function, non-spherical version

Estimate the anisotropic pcf function for second order reweighted ("inhomogeneous") pattern.

Usage

pcf_anin_fry(
  x,
  u,
  r,
  lambda = NULL,
  lambda_h,
  bw,
  stoyan = 0.35,
  renormalise = TRUE,
  border = 1,
  ...
)

Arguments

x

pp, list with $x~coordinates $bbox~bounding box

u

unit vector(s) of direction, as row vectors. Default: x and y axis.

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)

bw

smoothing bandwidth for multi-dimensional epanechnikov kernel.

stoyan

If r_h not given, use bw=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.

...

passed on to e.g. intensity_at_points

Value

Returns a dataframe.

Details

Computes a second order reweighted version of the anisotropic pcf. Essentially the estimate of intensity of pairwise vectors at locations outer(r, u). We will use antipodal estimation, so directions should not include antipodal pairs.

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'.

See also

pcf_anin_sector, pcf_anin_cylinder