In this context, the observed dataset may consist of the times of occurrence of predefined events, such as earthquakes in a given region over a given magnitude, or of the locations in geographical space of plants of a given species.
[2] A different definition applies for a dispersion index for intervals,[3] where the quantities treated are the lengths of the time-intervals between the events.
This yields the following table: This can be considered analogous to the classification of conic sections by eccentricity; see Cumulants of particular probability distributions for details.
When the coefficient of dispersion is less than 1, a dataset is said to be "under-dispersed": this condition can relate to patterns of occurrence that are more regular than the randomness associated with a Poisson process.
A sample-based estimate of the dispersion index can be used to construct a formal statistical hypothesis test for the adequacy of the model that a series of counts follow a Poisson distribution.
Therefore, to assess if a given spatial pattern (assuming you have a way to measure it) is due purely to diffusion or if some particle-particle interaction is involved : divide the space into patches, Quadrats or Sample Units (SU), count the number of individuals in each patch or SU, and compute the VMR.
VMRs significantly higher than 1 denote a clustered distribution, where random walk is not enough to smother the attractive inter-particle potential.
Iowa, New York and South Dakota use this linear coefficient of dispersion to estimate dues taxes.