
204 Spatial Point Patterns: Methodology and Applications with R
The con tribution from each data point x
i
to the sum in (7.2 ) is
t
i
(r) =
∑
j6=i
1
d
i j
≤ r
,
the number of other data points x
j
which lie closer than a distance r. We might call this the number
of r-neighbours for the point x
i
. Equivalently t
i
(r) is the number of data points which fall inside a
circle of radius r centred at x
i
, not counting x
i
itself. Then
b
H(r) =
1
n(n −1)
n
∑
i=1
t
i
(r) =
1
n −1
t(r)
where
t(r) = (1/n)
∑
i
t
i
(r) is the average number of r-neighbours per data point.
Figure 7.5. Counting r-neighbou rs. In
each circle, the numeral shows the value
of t
i
(r) for the data point x
i
at the cen ...