Exploring spatial point patterns - Spatial Data Analysis: An Introduction for GIS Users - page 98

where n is the number of events and d min is the distance from the nearest event. In
words, the distance of each event i at location x i to its nearest neighbour and the aver-
age of these distances are computed. h ese statistics are used to compute two other
measures called the G and F functions, which will be described next.
h e G and F functions allow the exploration of event to event nearest-neighbour
distances. h e G function is dei ned as the cumulative frequency distribution of the
nearest-neighbour distances. It is given by:

#( d ( x ) < d )

min i

(7.10)

Gd () =

n

In words, G ( d ) gives the proportion (since the count is divided by n ) of nearest-neighbour
distances that are less than distance d . Obtaining G for dif erent values of d enables
assessment of the degree of clustering at dif erent spatial scales. For example, for a
clustered point pattern, G will increase markedly as distance increases for small dis-
tances. For a regular point pattern the increase will be more gradual. Figure 7.12
shows the G function for the point patterns in Figures 7.1 (PP1) and 7.2 (PP2) for
distance steps of 2.5 units. Clearly, the values of G for PP1 are larger at smaller dis-
tances than they are for PP2, indicating the greater degree of clustering in PP1 than in
PP2. A value of 1 for G corresponds to distances that are larger than the maximum
nearest-neighbour distance for a given point pattern. In other words, for PP1, no
nearest-neighbour distance is greater than 15 units, while for PP2 no nearest-neighbour
distance is greater than 12.5 units.
h e F function is similar to the G function, but instead of the events a sample
of point locations is selected randomly from anywhere in the study area—that is,

1

0.9

PP 1
PP 2 0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 5 10 15 20

Distance

Figure 7.12 G function for the point patterns in Figures 7.1 (PP1) and 7.2 (PP2).