# Hardcore: The Hard Core Point Process Model

### Description

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

### Usage

 `1` ``` Hardcore(hc=NA) ```

### Arguments

 `hc` The hard core distance

### Details

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,…,x_n) = alpha . beta^n(x)

where x[1],…,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.

### Value

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

and \rolf

### References

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.

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

### Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ``` Hardcore(0.02) # prints a sensible description of itself ## Not run: ppm(cells, ~1, Hardcore(0.05)) # fit the stationary hard core process to `cells' ## End(Not run) # estimate hard core radius from data ppm(cells, ~1, Hardcore()) ppm(cells, ~1, Hardcore) ppm(cells, ~ polynom(x,y,3), Hardcore(0.05)) # fit a nonstationary hard core process # with log-cubic polynomial trend ```

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