Tstat: Third order summary statistic
Description
Computes the third order summary statistic $T(r)$
of a spatial point pattern.Usage
Tstat(X, ..., r = NULL, rmax = NULL,
correction = c("border", "translate"), ratio = FALSE, verbose=TRUE)Arguments
X
The observed point pattern,
from which an estimate of $T(r)$ will be computed.
An object of class "ppp", or data
in any format acceptable to as.ppp(). r
Optional. Vector of values for the argument $r$ at which $T(r)$
should be evaluated. Users are advised not to specify this
argument; there is a sensible default.
rmax
Optional. Numeric. The maximum value of $r$ for which
$T(r)$ should be estimated.
correction
Optional. A character vector containing any selection of the
options "none", "border", "bord.modif",
"translate", "translation", or "best".
It specifies the edge cor
ratio
Logical.
If TRUE, the numerator and denominator of
each edge-corrected estimate will also be saved,
for use in analysing replicated point patterns.
verbose
Logical. If TRUE, an estimate of the computation time
is printed.
Value
- An object of class
"fv", see fv.object,
which can be plotted directly using plot.fv.
Computation time
If the number of points is large, the algorithm can take a very long time
to inspect all possible triangles. A rough estimate
of the total computation time will be printed at the beginning
of the calculation. If this estimate seems very large,
stop the calculation using the user interrupt signal, and
call Tstat again, using rmax to restrict the
range of r values,
thus reducing the number of triangles to be inspected.Details
This command calculates the
third-order summary statistic $T(r)$ for a spatial point patterns,
defined by Schladitz and Baddeley (2000). The definition of $T(r)$ is similar to the definition of Ripley's
$K$ function $K(r)$, except that $K(r)$ counts pairs of
points while $T(r)$ counts triples of points.
Essentially $T(r)$ is a rescaled cumulative
distribution function of the diameters of triangles in the
point pattern. The diameter of a triangle is the length of its
longest side.
References
Schladitz, K. and Baddeley, A. (2000)
A third order point process characteristic.
Scandinavian Journal of Statistics 27 (2000) 657--671.