Myriam Elizabeth Saavedra López - Repositorio Digital USFQ ...

(sub-section 4.3.2).
The presence of deviations between all the estimates and the Kpois(r) curves in ‘a’ panel suggests
spatial clustering because the various estimate curves tend to be greater than the theoretical curve
(Cressie, 1993). In the ‘b’ panel, the observations curve is under the CSR simulations envelope,
but when the radius is equal to and greater than 297 meters, the observations curve is greater than
hi(r) curve, hence the null hypothesis cannot be accepted and it is possible to have spatial clustering
with radiuses equal to and greater than 297 meters (see definition of Simulation Envelopes). Another
possible conclusion could be that there are dependent interactions between the points inside the ball
when radiuses are equal to or greater than 297 meters.
4.3.4 First and second moment characteristic analysis for I
To support or to discard the results from the Estimates of the Empty Space Function F and of the
Nearest Neighbour Distance Function G (First Moment Characteristic), it is recommended to apply
the Estimate the Function J in the spatial analysis of the data set. With the same criterion, it is
also recommended to use the Pair Correlation Functiong to support or to discard the results of the
Estimate of the Function K (Second Moment Characteristic).
4.3.4.1 Estimate the function J According to section ‘3.4.3.’ and formula (19), the J (r) function
of a stationary point process is defined as: J (r) = 1−G(r)
1−F (r) where G (r) is the nearest neighbour distance
distribution function of the point process and F (r) is its Empty Space Function. For a completely
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