
Greenwood statistic
Encyclopedia
The Greenwood statistic is a spacing statistic and can be used to evaluate clustering of events in time or locations in space.

where
represents the interval between events or points in space and is a number between 0 and 1 such that the sum of all
.
Where intervals are given by numbers that do not represent a fraction of the time period or distance, the Greenwood statistic is modified and is given by:

where:

and
represents the length of the ith interval, which is either the time between events or the distances between points in space.
A reformulation of the statistic yields

where
is the sample coefficient of variation
of the n + 1 interval lengths.
Definition
In general, for a given sequence of events in time or space the statistic is given by:.
where


Where intervals are given by numbers that do not represent a fraction of the time period or distance, the Greenwood statistic is modified and is given by:

where:

and

A reformulation of the statistic yields

where

Coefficient of variation
In probability theory and statistics, the coefficient of variation is a normalized measure of dispersion of a probability distribution. It is also known as unitized risk or the variation coefficient. The absolute value of the CV is sometimes known as relative standard deviation , which is...
of the n + 1 interval lengths.