Low-level functions which calculate the estimated \(K\) function and estimated pair correlation function (or any similar functions) from a matrix of pairwise distances and optional weights.
compileK(D, r, weights = NULL, denom = 1,
check = TRUE, ratio = FALSE, fname = "K",
samplesize=denom)compilepcf(D, r, weights = NULL, denom = 1,
check = TRUE, endcorrect = TRUE, ratio=FALSE,
..., fname = "g", samplesize=denom)
An object of class "fv" representing the estimated function.
A square matrix giving the distances between all pairs of points.
An equally spaced, finely spaced sequence of distance values.
Optional numerical weights for the pairwise distances.
A numeric matrix with the same dimensions as D.
If absent, the weights are taken to equal 1.
Denominator for the estimator.
A single number, or a numeric vector with the same length
as r. See Details.
Logical value specifying whether to check that D is a
valid matrix of pairwise distances.
Logical value indicating whether to store ratio information. See Details.
Optional arguments passed to density.default
controlling the kernel smoothing.
Logical value indicating whether to apply End Correction of
the pair correlation estimate at r=0.
Character string giving the name of the function being estimated.
The sample size that should be used as the denominator when
ratio=TRUE.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
These low-level functions construct estimates of the \(K\) function or pair correlation function, or any similar functions, given only the matrix of pairwise distances and optional weights associated with these distances.
These functions are useful for code development and for teaching,
because they perform a common task, and do the housekeeping required to
make an object of class "fv" that represents the estimated
function. However, they are not very efficient.
compileK calculates the weighted estimate
of the \(K\) function,
$$
\hat K(r) = (1/v(r)) \sum_i \sum_j 1\{ d_{ij} \le r\} w_{ij}
$$
and compilepcf calculates the weighted estimate of the
pair correlation function,
$$
\hat g(r) = (1/v(r)) \sum_i \sum_j \kappa( d_{ij} - r ) w_{ij}
$$
where \(d_{ij}\) is the distance between spatial points
\(i\) and \(j\), with corresponding weight \(w_{ij}\),
and \(v(r)\) is a specified denominator. Here \(\kappa\)
is a fixed-bandwidth smoothing kernel.
For a point pattern in two dimensions, the usual denominator \(v(r)\) is constant for the \(K\) function, and proportional to \(r\) for the pair correlation function. See the Examples.
The result is an object of class "fv" representing the
estimated function. This object has only one column of function
values. Additional columns (such as a column giving the theoretical
value) must be added by the user, with the aid of
bind.fv.
If ratio=TRUE, the result also belongs to class "rat"
and has attributes containing the numerator and denominator
of the function estimate.
(If samplesize is given, the numerator and denominator are
rescaled by a common factor so that the denominator is
equal to samplesize.)
This allows function estimates from
several datasets to be pooled using pool.
Kest,
pcf for definitions of the \(K\) function
and pair correlation function.
bind.fv to add more columns.
X <- japanesepines
D <- pairdist(X)
Wt <- edge.Ripley(X, D)
lambda <- intensity(X)
a <- (npoints(X)-1) * lambda
r <- seq(0, 0.25, by=0.01)
K <- compileK(D=D, r=r, weights=Wt, denom=a)
g <- compilepcf(D=D, r=r, weights=Wt, denom= a * 2 * pi * r)
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