
Gibbs Mo dels 517
core. These parameters ca n be estimated immediately from data. The max imum likelihood estima-
tor of the hard core distance [58 1] is the minimum nearest-neighbourdistance d
min
= min
i
min
j6=i
d
i j
.
In spatstat we use th e modified estimator h
∗
= (n(x)/(n (x)+ 1))d
min
which has smaller bias and
avoids computational problems. If the user calls the f unction Hardcore without specifying the hard
core diameter h, then h will be estimated by calculating h
∗
for the point pattern data, and the model-
fitting will proceed with that value. Thus, the user has th e option to fit the har d core model with
an automatically estimated hard core radius