Meaning
Probability densities describe the likelihood of finding a point at a specific distance from another point relative to the average density of the entire set. Using a pair correlation function allows a researcher to identify specific scales where clustering or inhibition occurs without the cumulative bias found in other metrics. The value is calculated as the derivative of the k-function and represents the ratio of the observed intensity at a fixed distance to the expected intensity under randomness.
Distance Relationship
Values greater than one indicate that points are more likely to be found at that specific separation. This distance relationship reveals the characteristic spacing of objects.
Structural Insight
Peaks in the plot correspond to preferred distances between points. A pair correlation function provides a detailed view of the spatial structure by isolating interactions at discrete intervals. If a pattern shows a high peak at five millimeters and then a drop below one, it suggests that points tend to form pairs or clusters with that specific internal spacing.
This is different from cumulative functions which would average these effects over all smaller distances. The analysis is sensitive to small changes in point location and requires careful smoothing of the data.
Scale Sensitivity
Smoothing kernels are required to estimate the density from finite samples. A scale sensitivity is determined by the bandwidth chosen for the estimation.
