Hopkins statistic
The Hopkins statistic is a way of measuring the cluster tendency of a data set. 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. If individuals are aggregated, then its value approaches 1, and if they are randomly distributed along the value tends to 0.5.
Preliminaries
A typical formulation of the Hopkins statistic follows.Definition
With the above notation, if the data is dimensional, then the Hopkins statistic is defined as:Under the null hypotheses, this statistic has a Beta distribution.