pcf_anin: Inhomogeneous anisotropic pcf function, sector version

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

Inhomogeneous anisotropic pcf function, sector version

Description

Estimate a sector/cone pcf function for second order reweighted ("inhomogeneous") pattern.

Usage

pcf_anin(
  x,
  u,
  epsilon,
  r,
  lambda = NULL,
  lambda_h,
  r_h,
  stoyan = 0.15,
  renormalise = TRUE,
  border = 1,
  divisor = "d",
  ...
)

pcf_anin_conical(
  x,
  u,
  epsilon,
  r,
  lambda = NULL,
  lambda_h,
  r_h,
  stoyan = 0.15,
  renormalise = TRUE,
  border = 1,
  divisor = "d",
  ...
)

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	Central half angle for the directed sector/cone (total angle of the rotation cone is 2*epsilon)
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.
divisor	See spatstat's pcf.ppp for this.
...	passed on to e.g. intensity_at_points

Details

Computes a second order reweighted version of the sector-pcf. The sector pcf differs from the true anisotropic pcf by assuming that the anisotropic pcf is constant over the small arc/cap of the sector, thus averaging over that data-area and providing more stable estimates.

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

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_cylinder

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