pcf_anin_fry: Inhomogeneous anisotropic pcf function, non-spherical version

In antiphon/Kdirectional: Analysis of anisotropy in point patterns using second order statistics

Inhomogeneous anisotropic pcf function, non-spherical version

Description

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

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'.

Value

Returns a dataframe.

See Also

pcf_anin

antiphon/Kdirectional documentation built on Feb. 13, 2023, 6:26 a.m.