Myriam Elizabeth Saavedra López - Repositorio Digital USFQ ...

When the radius is 7.11 meters, the first contact distance appears, that means the cumulative empirical
distribution have value greater than 0 (information having by the summary of function Fest). When
the radius is greater than 70 meters; it is possible to observe the cumulative empirical distribution
approaching close to the lower simulation envelope, according to the deviation between the Kaplan-
Meier estimate function and the theoretical Poisson function. Additionally, looking at the results
of the ‘a’ panel (of Figure 2), the observations curve ‘Km(r)’ is always below the theoretical curve
with the only exception being when the radius is between 14.22 and 42.65 meters. The tendency
of the observation curve to be below the lower simulation curve when the radiuses are ascending,
may suggest the presence of clusters. However, it can be concluded from the results that: the null
hypothesis cannot be rejected because the cumulative empirical distribution of the observations in ‘b’
panel (distances or radiuses) falls within the CSR simulation envelope.
4.3.2 Estimation of the nearest neighbour distance function G
Whether the null hypothesis from the empty space function (or contact distance function) was not
rejected, then there is a high possibility that the Nearest Neighbour Function G will produce a similar
result. Once again, the Figure 3 presents two panels: Nearest Neighbour Distance function G and
Simulation Envelopes to G function under the same conditions, but the recommended range of the
radius is between 0 to 131.69 meters.
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