
Correlation 219
tor of the K-function,
b
K
trans
(r) =
1
λ
n
n
∑
i=1
n
∑
j=1
j6=i
1
d
i j
≤ r
|W |
|W ∩(W −(x
j
−x
i
))|
. (7.19)
In this estimator, each pair of data points (x
i
,x
j
) is weighted by the reciprocal of the fraction of
window ar ea in which the first data point x
i
could be placed so that both po ints x
i
,x
j
would be
observable (assuming their relative positions were held fixed). This effectively comp ensates for the
sampling bias in observing such pairs.
The edge correction weight in (7.19) can be calcula te d u sing simple geometry if W is a rect-
angle. Otherwise, the most efficient algorithm computes the set covariance function C
W
(v) =
|W ∩(W −v)| for all vectors ...