Hopkins statistic

The Hopkins statistic (introduced by Brian Hopkins and John Gordon Skellam) is a way of measuring the cluster tendency of a data set.

[1] It belongs to the family of sparse sampling tests.

It acts as a statistical hypothesis test where the null hypothesis is that the data is generated by a Poisson point process and are thus uniformly randomly distributed.

[2] If individuals are aggregated, then its value approaches 0, and if they are randomly distributed along the value tends to 0.5.

[3] A typical formulation of the Hopkins statistic follows.

Under the null hypotheses, this statistic has a Beta(m,m) distribution.