The Hard Core Point Process Model

Creates an instance of the hard core point process model which can then be fitted to point pattern data.

models, spatial
The hard core distance

A hard core process with hard core distance $h$ and abundance parameter $\beta$ is a pairwise interaction point process in which distinct points are not allowed to come closer than a distance $h$ apart.

The probability density is zero if any pair of points is closer than $h$ units apart, and otherwise equals $$f(x_1,\ldots,x_n) = \alpha \beta^{n(x)}$$ where $x_1,\ldots,x_n$ represent the points of the pattern, $n(x)$ is the number of points in the pattern, and $\alpha$ is the normalising constant.

The function ppm(), which fits point process models to point pattern data, requires an argument of class "interact" describing the interpoint interaction structure of the model to be fitted. The appropriate description of the hard core process pairwise interaction is yielded by the function Hardcore(). See the examples below.

If the hard core distance argument hc is missing or NA, it will be estimated from the data when ppm is called. The estimated value of hc is the minimum nearest neighbour distance multiplied by $n/(n+1)$, where $n$ is the number of data points.


  • An object of class "interact" describing the interpoint interaction structure of the hard core process with hard core distance hc.


Baddeley, A. and Turner, R. (2000) Practical maximum pseudolikelihood for spatial point patterns. Australian and New Zealand Journal of Statistics 42, 283--322.

Ripley, B.D. (1981) Spatial statistics. John Wiley and Sons.

See Also

Strauss, StraussHard, MultiHard, ppm, pairwise.family, ppm.object

  • Hardcore
   # prints a sensible description of itself


   ppm(cells, ~1, Hardcore(0.05))
   # fit the stationary hard core process to `cells'

   ppm(cells, ~1, Hardcore())

   ppm(cells, ~ polynom(x,y,3), Hardcore(0.05))
   # fit a nonstationary hard core process
   # with log-cubic polynomial trend
Documentation reproduced from package spatstat, version 1.41-1, License: GPL (>= 2)

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