G3est
Nearest Neighbour Distance Distribution Function of a Three-Dimensional Point Pattern
Estimates the nearest-neighbour distance distribution function $G_3(r)$ from a three-dimensional point pattern.
- Keywords
- spatial, nonparametric
Usage
G3est(X, ..., rmax = NULL, nrval = 128, correction = c("rs", "km", "Hanisch"))Arguments
- X
- Three-dimensional point pattern (object of class
"pp3"). - ...
- Ignored.
- rmax
- Optional. Maximum value of argument $r$ for which $G_3(r)$ will be estimated.
- nrval
- Optional. Number of values of $r$ for which
$G_3(r)$ will be estimated. A large value of
nrvalis required to avoid discretisation effects. - correction
- Optional. Character vector specifying the edge correction(s) to be applied. See Details.
Details
For a stationary point process $\Phi$ in three-dimensional
space, the nearest-neighbour function
is
$$G_3(r) = P(d^\ast(x,\Phi) \le r \mid x \in \Phi)$$
the cumulative distribution function of the distance
$d^\ast(x,\Phi)$ from a typical point $x$
in $\Phi$ to its nearest neighbour, i.e.
to the nearest other point of $\Phi$.
The three-dimensional point pattern X is assumed to be a
partial realisation of a stationary point process $\Phi$.
The nearest neighbour function of $\Phi$ can then be estimated using
techniques described in the References. For each data point, the
distance to the nearest neighbour is computed.
The empirical cumulative distribution
function of these values, with appropriate edge corrections, is the
estimate of $G_3(r)$.
The available edge corrections are: [object Object],[object Object],[object Object]
Value
- A function value table (object of class
"fv") that can be plotted, printed or coerced to a data frame containing the function values.
Warnings
A large value of nrval is required in order to avoid
discretisation effects (due to the use of histograms in the
calculation).
References
Baddeley, A.J, Moyeed, R.A., Howard, C.V. and Boyde, A. (1993) Analysis of a three-dimensional point pattern with replication. Applied Statistics 42, 641--668.
Baddeley, A.J. and Gill, R.D. (1997) Kaplan-Meier estimators of interpoint distance distributions for spatial point processes. Annals of Statistics 25, 263--292.
Hanisch, K.-H. (1984) Some remarks on estimators of the distribution function of nearest neighbour distance in stationary spatial point patterns. Mathematische Operationsforschung und Statistik, series Statistics 15, 409--412.
See Also
Examples
X <- rpoispp3(42)
Z <- G3est(X)
if(interactive()) plot(Z)