hopkins-statistic¶

hopkins-statistic is a library for computing the Hopkins statistic to assess clustering tendency (also known as clusterability) by testing for departure from complete spatial randomness (CSR) in point patterns.

This implementation defaults to the Cross and Jain (1982) formulation, raising distances to the power of the data dimension. In two dimensions, this matches the original definition by Hopkins and Skellam (1954). Because the resulting statistic follows a beta distribution under the null hypothesis, p-values can be computed analytically, avoiding the need for Monte Carlo simulations.

Installation¶

pipuv (project)uv (environment)

pip install hopkins-statistic

uv add hopkins-statistic

uv pip install hopkins-statistic

Usage¶

Hopkins statisticHopkins test

import numpy as np
from hopkins_statistic import hopkins

rng = np.random.default_rng(42)
X = rng.uniform(size=(100, 2))

print(hopkins(X, rng=rng))

0.5137976176502288

import numpy as np
from hopkins_statistic import hopkins_test

rng = np.random.default_rng(42)
X = rng.uniform(size=(100, 2))

print(hopkins_test(X, rng=rng))

HopkinsTestResult(statistic=0.5137976176502288, pvalue=0.45148888266508536)