Hest: Spherical Contact Distribution Function

Description

Estimates the spherical contact distribution function of a random set.

Usage

Hest(X, ...)

Arguments

The observed random set. An object of class "ppp", "psp" or "owin".

...

Arguments passed to as.mask to control the discretisation.

Value

An object of class "fv", see fv.object, which can be plotted directly using plot.fv.
Essentially a data frame containing five columns:
rthe values of the argument $r$ at which the function $H(r)$ has been estimated
rsthe ``reduced sample'' or ``border correction'' estimator of $H(r)$
kmthe spatial Kaplan-Meier estimator of $H(r)$
hazardthe hazard rate $\lambda(r)$ of $H(r)$ by the spatial Kaplan-Meier method
rawthe uncorrected estimate of $H(r)$, i.e. the empirical distribution of the distance from a fixed point in the window to the nearest point of X

Details

The spherical contact distribution function of a stationary random set $X$ is the cumulative distribution function $H$ of the distance from a fixed point in space to the nearest point of $X$, given that the point lies outside $X$. That is, $H(r)$ equals the probability that X lies closer than $r$ units away from the fixed point $x$, given that X does not cover $x$.

For a point process, the spherical contact distribution function is the same as the empty space function $F$ discussed in Fest.

For Hest, the argument X may be a point pattern (object of class "ppp"), a line segment pattern (object of class "psp") or a window (object of class "owin"). It is assumed to be a realisation of a stationary random set.

The algorithm first calls distmap to compute the distance transform of X, then computes the Kaplan-Meier and reduced-sample estimates of the cumulative distribution following Hansen et al (1999).

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. The empty space hazard of a spatial pattern. Research Report 1994/3, Department of Mathematics, University of Western Australia, May 1994.

Hansen, M.B., Baddeley, A.J. and Gill, R.D. First contact distributions for spatial patterns: regularity and estimation. Advances in Applied Probability 31 (1999) 15-33.

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.

Examples

Run this code

X <- runifpoint(42)
   H <- Hest(X)
   Y <- rpoisline(10)
   H <- Hest(Y)
   data(heather)
   H <- Hest(heather$medium)

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