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. [2]
With the above notation, if the data is dimensional, then the Hopkins statistic is defined as: [4]
Under the null hypotheses, this statistic has a Beta(m,m) distribution.
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