R: (cross) pair correlation functions with a global intensity...

pcfglobal {globalKinhom}

R Documentation

(cross) pair correlation functions with a global intensity reweighting

Description

Compute g_\textrm{global} or c_\textrm{global}

Usage

pcfglobal(X, lambda=NULL, ..., sigma=bw.CvL(X), r=NULL, rmax=NULL,
    kernel="epanechnikov", bw=NULL, stoyan=0.15, normtol=.005, ratio=FALSE,
    discrete.lambda=FALSE, divisor=c("r", "d"),
    leaveoneout=TRUE, interpolate=TRUE, interpolate.fac=10, exp_prs=NULL,
    interpolate.maxdx=diameter(as.owin(X))/100, dump=FALSE)

pcfcross.global(X,Y, lambdaX=NULL, lambdaY=NULL, ...,
    sigma=bw.CvL(X), r=NULL, rmax=NULL, kernel="epanechnikov", bw=NULL,
    stoyan=0.15, normtol=.005, ratio=FALSE, discrete.lambda=FALSE,
    divisor=c("r", "d"), analytical=NULL, interpolate=TRUE,
    interpolate.fac=10, exp_prs=NULL,
    interpolate.maxdx=diameter(as.owin(X))/100, dump=FALSE)

Arguments

`X`, `Y`	point process of type `ppp`, on which to evaluate the (cross) `K`-function
`lambda`, `lambdaX`, `lambdaY`	intensity function estimates corresponding to `X` and `Y`. If omitted, intensity functions will be computed using `density.ppp` or `densityfun.ppp` (see discrete.lambda below)
`...`	extra args passed to density.ppp or densityfun.ppp, if applicable.
`sigma`	Bandwidth value to use for kernel-based intensity estimation, intensity functions and `exp_prs` are not provided by the user.
`r`	Values of `r` to evaluate `K(r)` at. If omitted, a sensible default is chosen, using the same conventions as `Kest` and `Kinhom`.
`rmax`	Maximum `r` to evaluate `K(r)` at. `rmax` is used to generate values for `r`, if omitted. If missing, a sensible default is chosen.
`kernel`	Kernel type for smoothing of pcf.
`bw`	Kernel bandwidth for smoothing of pcf.
`stoyan`	Coefficient for Stoyan's bandwidth selection rule. See `pcf.ppp`.
`normtol`	A tolerance to use for expectedPairs or expectedCrossPairs when computing monte-carlo estimates of the normalizing factor `\gamma`. Expressed as a maximum fractional standard error.
`ratio`	If `TRUE`, assemble numerator and denominator of pcf estimator separately.
`divisor`	Whether to use the evaluation distance (`"r"`) or the distance between points (`"d"`) to normalize the contribution of each point pair.
`analytical`	If `TRUE`, use Diggle-Jones weights
`discrete.lambda`	If `TRUE`, and intensity function(s) are not supplied, estimate intensities by interpolating the values on a discrete lattice (using `interp.im` and `density.ppp`), instead of exactly (using `densityfun.ppp`).
`interpolate`	If `TRUE`, evaluate the expectedCrossPairs on a lattice and interpolate, rather than at the exact displacements observed in the pattern.
`interpolate.fac`	If `interpolate`, the lattice spacing will be `sigma/interpolate.fac`.
`leaveoneout`	Use the leave-one-out estimator for `\gamma`. See Shaw et al 2020 for details.
`exp_prs`	A function that returns values for `\gamma_\textrm{iso}(r)`. If `\gamma` is known explicitly, or the same calculation is being used for several point patterns, it can be much faster to compute it once and provide the function as `exp_prs`, since the computation of `\gamma` is usually the slowest part.
`interpolate.maxdx`	Upper bound on allowable lattice spacing for interpolation.
`dump`	For debugging purposes, include computed values of `\gamma` with the output, as `attr`s.

Value

The return value is an object of class fv, just as for pcf and pcfinhom. The object contains columns r, theo, and global, corresponding respectively to the argument r, the theoretical values of g(r) for a Poisson process, and g_\mathrm{global}(r).

Author(s)

Thomas Shaw <shawtr@umich.edu>

References

T Shaw, J Møller, R Waagepetersen. 2020. “Globally Intensity-Reweighted Estimators for K- and pair correlation functions”. arXiv:2004.00527 [stat.ME].

Examples

rho <- funxy(function(x,y) 80*(1+x), owin())
X <- rpoispp(rho)
g <- pcfglobal(X)
#plot(g)

[Package globalKinhom version 0.1.8 Index]