The dip test of unimodality. (English) Zbl 0575.62045

Hartigan, J. A.; Hartigan, P. M.

Ann. Stat. 13, 70-84 (1985).

The dip test measures multimodality in a sample by the maximum difference, over all sample points, between the empirical distribution function, and the unimodal distribution function that minimizes that maximum difference. The uniform distribution is the asymptotically least favorable unimodal distribution, and the distribution of the test statistic is determined asymptotically and empirically when sampling from the uniform.

MSC:

62G10	Nonparametric hypothesis testing
62G05	Nonparametric estimation
62G30	Order statistics; empirical distribution functions
62F05	Asymptotic properties of parametric tests

Keywords:

isotonic regression; dip test; multimodality; empirical distribution; unimodal distribution; asymptotically least favorable unimodal distribution

Software:

dip