View source: R/Kest_anin_cylinder.R
Kest_anin_cylinder | R Documentation |
Estimate a cylinder-K function for second order reweighted ("inhomogeneous") pattern.
Kest_anin_cylinder( x, u, epsilon, r, lambda = NULL, lambda_h, renormalise = TRUE, border = 1, aspect = 1/3, ... )
x |
pp, list with $x~coordinates $bbox~bounding box |
u |
unit vector(s) of direction, as row vectors. Default: x and y axes, viz. c(1,0) and c(0,1). |
epsilon |
The cylinder half-width. Will be extended to the length of r, so can be given per r. |
r |
radius vector at which to evaluate K |
lambda |
optional vector of intensity estimates at points |
lambda_h |
if lambda missing, use this bandwidth in a kernel estimate of lambda(x) |
renormalise |
See details. |
border |
Use border correction? Default=1, yes. |
aspect |
Instead of using a fixed halfwidth (epsilon) take the halfwidth to be 'aspect * r/2' (so an increasing vector). Default : 1/3 |
... |
passed on to e.g. intensity_at_points |
Computes a second order reweighted version of the cylinder-K. In short, we count how many pairs of points in the pattern has both a) their difference vector inside a cylinder with major-axial direction 'u' and radius epsilon, and b) difference vector length less than range r. Usually r is a vector and the output is then a vector as well.
Note the default behaviour is to use a fixed aspect ratio cylinder with aspect = 2*epsilon/range = 1/3.
An estimate of the intensity Lambda(x) at points can be given ('lambda'). If it is a single value, the pattern is assumed to be homogeneous.
If it is a vector the same length as there are points, the pattern is taken to be second-order stationary. In this case the
the sum over the pairs (i,j) is weighted with 1/(lambda[i]*lambda[j]). If 'lambda' is missing, 'lambda_h', a single positive number,
should be given, which is then used for estimating the non-constant Lambda(x) via Epanechnikov kernel smoothing (see intensity_at_points).
If 'renormalise=TRUE', we normalise the intensity estimate so that sum(1/lambda(x))=|W|. This corresponds in spatstat
's Kinhom
to setting 'normpower=2'.
About border correction: If x$bbox is a a simple bounding box, the algorithm uses the translation corrected weighting 1/area(Wx intersect Wy) with Wx=W+x. If x$bbox is a bbquad-object, for example rotated polygon, the algorithm uses simple minus border correction.
Returns a dataframe.
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