# OrdThresh

0th

Percentile

##### Ord's Interaction model

Creates an instance of Ord's point process model which can then be fitted to point pattern data.

Keywords
models, spatial
##### Usage
OrdThresh(r)
##### Arguments
r

Positive number giving the threshold value for Ord's model.

##### Details

Ord's point process model (Ord, 1977) is a Gibbs point process of infinite order. Each point $x_i$ in the point pattern $x$ contributes a factor $g(a_i)$ where $a_i = a(x_i, x)$ is the area of the tile associated with $x_i$ in the Dirichlet tessellation of $x$. The function $g$ is simply $g(a) = 1$ if $a \ge r$ and $g(a) = \gamma < 1$ if $a < r$, where $r$ is called the threshold value.

This function creates an instance of Ord's model with a given value of $r$. It can then be fitted to point process data using ppm.

##### Value

An object of class "interact" describing the interpoint interaction structure of a point process.

##### References

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

Ord, J.K. (1977) Contribution to the discussion of Ripley (1977).

Ord, J.K. (1978) How many trees in a forest? Mathematical Scientist 3, 23--33.

Ripley, B.D. (1977) Modelling spatial patterns (with discussion). Journal of the Royal Statistical Society, Series B, 39, 172 -- 212.

ppm, ppm.object