Points are distributed following a complete spatial randomness (CSR) pattern if events are equally likely to occur anywhere within an area. There are two types departure from a CSR: regularity and clustering. Figure 1 gives an example of a complete random, regular and a clustered pattern.
Various indices and statistics measure departure from CSR. The v.qcount function implements six different quadrat count indices that are described in Cressie (1991; p. 590-591) and in Ripley (1981; p. 102-106) and summarized in Table 1.
These indices are computed as follows: v.qcount chooses nquadrads circular quadrats of radius radius such that they are completely within the bounds of the current region and no two quadrats overlap. The number of points falling within each quadrat are counted and indices are calculated to estimate the departure of point locations from complete spatial randomness. This is illustrated in Figure 2.
The number of points is written as category to the output map (and not to an attribute table).v.random, v.distance, v.neighbors, v.perturb
 Noel A. C. Cressie. Statistics for Spatial Data. Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons, New York, NY, 1st edition, 1991.
 Brian D. Ripley. Spatial Statistics. John Wiley \& Sons, New York, NY, 1981.
References to the indices include:
 R. A. Fisher, H. G. Thornton, and W. A. Mackenzie. The accuracy of the plating method of estimating the density of bacterial populations. Annals of Applied Biology, 9:325-359, 1922.
 F. N. David and P. G. Moore. Notes on contagious distributions in plant populations. Annals of Botany, 18:47-53, 1954.
 J. B. Douglas. Clustering and aggregation. Sankhya B, 37:398-417, 1975.
 M. Lloyd. Mean crowding. Journal of Animal Ecology, 36:1-30, 1967.
 M. Morista. Measuring the dispersion and analysis of distribution patterns. Memoires of the Faculty of Science, Kyushu University, Series E. Biology, 2:215-235, 1959.
A more detailed background is given in the tutorial:
 James Darrell McCauley 1993. Complete Spatial Randomness and Quadrat Methods - GRASS Tutorial on v.qcountJames Darrell McCauley
Modified for GRASS 5.0 by Eric G. Miller (2000-10-28)
Modified for GRASS 5.7 by R. Blazek (2004-10-14)
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© 2003-2022 GRASS Development Team, GRASS GIS 7.8.8dev Reference Manual