THE DIP TEST OF UNIMODALITY

THE DIP TEST OF UNIMODALITY

1985, Vol. 13, No. 1, 70–84 | J. A. HARTIGAN AND P. M. HARTIGAN
The dip test, proposed by J. A. Hartigan and P. M. Hartigan, is a statistical method for detecting multimodality in a sample by measuring the maximum difference between the empirical distribution function and the unimodal distribution function that minimizes this difference. The uniform distribution is chosen as the null distribution, and the asymptotic distribution of the dip statistic is derived. The test is consistent for testing any unimodal distribution against any multimodal distribution. The paper discusses the theoretical properties of the dip test, including its asymptotic behavior, computational methods, and power comparisons with other tests. The dip test is shown to be more effective than the likelihood ratio test and the depth test in detecting bimodality, especially in cases with pronounced tails. The paper also provides an example of applying the dip test to assess faculty quality in statistics departments and discusses its extension to multivariate data through the minimum spanning tree.The dip test, proposed by J. A. Hartigan and P. M. Hartigan, is a statistical method for detecting multimodality in a sample by measuring the maximum difference between the empirical distribution function and the unimodal distribution function that minimizes this difference. The uniform distribution is chosen as the null distribution, and the asymptotic distribution of the dip statistic is derived. The test is consistent for testing any unimodal distribution against any multimodal distribution. The paper discusses the theoretical properties of the dip test, including its asymptotic behavior, computational methods, and power comparisons with other tests. The dip test is shown to be more effective than the likelihood ratio test and the depth test in detecting bimodality, especially in cases with pronounced tails. The paper also provides an example of applying the dip test to assess faculty quality in statistics departments and discusses its extension to multivariate data through the minimum spanning tree.
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