
290 Spatial Point Patterns: Methodology and Applications with R
duplicated values to obtain the sequence s
1
< s
2
< ··· < s
k
of unique distances, the n taking the
product over these values s
j
.
To understand the rationale for (8.41), notice that the denominator #{i :
e
t
i
≥ s} is the numbe r
of p oints x
i
which are ‘still alive at time s’, while the numerator #{i :
e
t
i
= s, d
i
= 1} is the number
of points which are ‘observed to die at time s’. The ratio of these numbers is an estimate of the
conditional probability of dying exactly at time s given survival at least to time s. The term in
parenthe ses is an estimate of the probability o f surviving longer than ...