# Gest

0th

Percentile

##### Nearest Neighbour Distance Function G

Estimates the nearest neighbour distance distribution function $G(r)$ from a point pattern in a window of arbitrary shape.

Keywords
spatial, nonparametric
##### Usage
Gest(X, r=NULL, breaks=NULL, ..., correction=c("rs", "km", "han"))
##### Arguments
X
The observed point pattern, from which an estimate of $G(r)$ will be computed. An object of class ppp, or data in any format acceptable to as.ppp().
r
Optional. Numeric vector. The values of the argument $r$ at which $G(r)$ should be evaluated. There is a sensible default. First-time users are strongly advised not to specify this argument. See below for important conditions on $r$.
breaks
An alternative to the argument r. Not normally invoked by the user. See the Details section.
...
Ignored.
correction
Optional. The edge correction(s) to be used to estimate $G(r)$. A vector of character strings selected from "none", "rs", "km", "Hanisch" and "best".
##### Details

The nearest neighbour distance distribution function (also called the event-to-event'' or inter-event'' distribution) of a point process $X$ is the cumulative distribution function $G$ of the distance from a typical random point of $X$ to the nearest other point of $X$.

An estimate of $G$ derived from a spatial point pattern dataset can be used in exploratory data analysis and formal inference about the pattern (Cressie, 1991; Diggle, 1983; Ripley, 1988). In exploratory analyses, the estimate of $G$ is a useful statistic summarising one aspect of the clustering'' of points. For inferential purposes, the estimate of $G$ is usually compared to the true value of $G$ for a completely random (Poisson) point process, which is $$G(r) = 1 - e^{ - \lambda \pi r^2}$$ where $\lambda$ is the intensity (expected number of points per unit area). Deviations between the empirical and theoretical $G$ curves may suggest spatial clustering or spatial regularity.

##### References

Baddeley, A.J. Spatial sampling and censoring. In O.E. Barndorff-Nielsen, W.S. Kendall and M.N.M. van Lieshout (eds) Stochastic Geometry: Likelihood and Computation. Chapman and Hall, 1998. Chapter 2, pages 37-78. Baddeley, A.J. and Gill, R.D. Kaplan-Meier estimators of interpoint distance distributions for spatial point processes. Annals of Statistics 25 (1997) 263-292.

Cressie, N.A.C. Statistics for spatial data. John Wiley and Sons, 1991.

Diggle, P.J. Statistical analysis of spatial point patterns. Academic Press, 1983.

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. Ripley, B.D. Statistical inference for spatial processes. Cambridge University Press, 1988.

Stoyan, D, Kendall, W.S. and Mecke, J. Stochastic geometry and its applications. 2nd edition. Springer Verlag, 1995.

nndist, nnwhich, Fest, Jest, Kest, km.rs, reduced.sample, kaplan.meier

##### Aliases
• Gest
• nearest.neighbour
##### Examples
data(cells)
G <- Gest(cells)
plot(G)

# P-P style plot
plot(G, cbind(km,theo) ~ theo)

# the empirical G is below the Poisson G,
# indicating an inhibited pattern

plot(G, . ~ r)
plot(G, . ~ theo)
plot(G, asin(sqrt(.)) ~ asin(sqrt(theo)))
Documentation reproduced from package spatstat, version 1.16-3, License: GPL (>= 2)

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