autoemx.utils.unimodality module

Hartigan’s dip test of unimodality.

Implemented from the method described in:

J. A. Hartigan and P. M. Hartigan, “The Dip Test of Unimodality”, The Annals of Statistics 13(1), 70-84 (1985).

The dip of a sample is the largest distance between its empirical distribution function and the closest unimodal distribution function. It is computed by shrinking a candidate modal interval: on its left the unimodal fit is the greatest convex minorant (GCM) of the empirical distribution, on its right the least concave majorant (LCM). The p-value is the fraction of uniform samples of the same size (the least favourable unimodal distribution) with a larger dip.

autoemx.utils.unimodality.dip_statistic(values) → float

Hartigan’s dip statistic of a 1D sample (between 1/(2n) and 1/4; larger means less unimodal).

Tied values are handled as a single point with the combined weight of its copies.

autoemx.utils.unimodality.dip_test(values, n_sims: int = 2000, seed: int = 0) → Tuple[float, float]

Hartigan’s dip test of unimodality.

Returns the dip statistic and the p-value: the fraction of uniform samples of the same size whose dip is at least as large. Small p-values (e.g. < 0.05) indicate more than one mode.