spatstat (version 1.17-1)

Hest: Spherical Contact Distribution Function

Description

Estimates the spherical contact distribution function of a random set.

Usage

Hest(X, ...)

Arguments

X

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:

• r
  the values of the argument $r$ at which the function $H(r)$ has been estimated
• rs
  the ``reduced sample'' or ``border correction'' estimator of $H(r)$
• km
  the spatial Kaplan-Meier estimator of $H(r)$
• hazard
  the hazard rate $\lambda(r)$ of $H(r)$ by the spatial Kaplan-Meier method
• raw
  the 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.

See Also

Fest

Examples

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