# Hardcore

##### 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.

##### Usage

`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 $$ f(x_1,\ldots,x_n) = \alpha \beta^{n(x)} $$ 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.

##### Value

An object of class `"interact"`

describing the interpoint interaction
structure of the hard core
process with hard core distance `hc`

.

##### 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.

##### See Also

`Strauss`

,
`StraussHard`

,
`MultiHard`

,
`ppm`

,
`pairwise.family`

,
`ppm.object`

##### Examples

```
# NOT RUN {
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'
# }
# 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
# }
```

*Documentation reproduced from package spatstat, version 1.59-0, License: GPL (>= 2)*