rStrauss(beta, gamma = 1, R = 0, W = owin(), expand=TRUE, nsim=1, drop=TRUE)
"owin"
) in which to
generate the random pattern.FALSE
, simulation is performed
in the window W
, which must be rectangular.
If TRUE
(the default), simulation is performed
on a larger window, and the result is clipped to the original
windnsim=1
and drop=TRUE
(the default), the
result will be a point pattern, rather than a list
containing a point pattern.W
using a The Strauss process (Strauss, 1975; Kelly and Ripley, 1976)
is a model for spatial inhibition, ranging from
a strong `hard core' inhibition to a completely random pattern
according to the value of gamma
.
The Strauss process with interaction radius $R$ and parameters $\beta$ and $\gamma$ is the pairwise interaction point process with probability density $$f(x_1,\ldots,x_n) = \alpha \beta^{n(x)} \gamma^{s(x)}$$ where $x_1,\ldots,x_n$ represent the points of the pattern, $n(x)$ is the number of points in the pattern, $s(x)$ is the number of distinct unordered pairs of points that are closer than $R$ units apart, and $\alpha$ is the normalising constant. Intuitively, each point of the pattern contributes a factor $\beta$ to the probability density, and each pair of points closer than $r$ units apart contributes a factor $\gamma$ to the density.
The interaction parameter $\gamma$ must be less than or equal to $1$ in order that the process be well-defined (Kelly and Ripley, 1976). This model describes an ``ordered'' or ``inhibitive'' pattern. If $\gamma=1$ it reduces to a Poisson process (complete spatial randomness) with intensity $\beta$. If $\gamma=0$ it is called a ``hard core process'' with hard core radius $R/2$, since no pair of points is permitted to lie closer than $R$ units apart.
The simulation algorithm used to generate the point pattern
is rmh
, whose output
is only approximately correct).
There is a tiny chance that the algorithm will
run out of space before it has terminated. If this occurs, an error
message will be generated.
}
nsim = 1
, a point pattern (object of class "ppp"
).
If nsim > 1
, a list of point patterns.
Berthelsen, K.K. and
Kelly, F.P. and Ripley, B.D. (1976) On Strauss's model for clustering. Biometrika 63, 357--360.
Strauss, D.J. (1975)
A model for clustering.
Biometrika 62, 467--475.
}
[object Object],[object Object]
rmh
,
Strauss
,
rHardcore
,
rStraussHard
,
rDiggleGratton
,
rDGS
,
rPenttinen
.