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 is a statistical method for detecting multimodality in a distribution by measuring the maximum difference between the empirical distribution function and the unimodal distribution that minimizes this difference. The test is based on the uniform distribution, which is asymptotically least favorable for unimodal distributions. The dip statistic is defined as the maximum difference between the empirical distribution function and the best-fitting unimodal distribution. It can be computed in linear time and is consistent for testing unimodal against multimodal distributions. The dip statistic is asymptotically distributed as a Brownian bridge when the data is uniformly distributed. The test is robust to the normality assumption and is not sensitive to the choice of kernel width. The dip test is compared with other tests for multimodality, such as the likelihood ratio test and the depth test, and is found to be more powerful. The dip test is also extended to the multivariate case using the minimum spanning tree. The test is applied to real data, such as the quality of faculty in statistics departments, and is shown to detect multimodality effectively. The dip test is a useful tool for detecting multimodality in data and is recommended for use in statistical analysis.The dip test is a statistical method for detecting multimodality in a distribution by measuring the maximum difference between the empirical distribution function and the unimodal distribution that minimizes this difference. The test is based on the uniform distribution, which is asymptotically least favorable for unimodal distributions. The dip statistic is defined as the maximum difference between the empirical distribution function and the best-fitting unimodal distribution. It can be computed in linear time and is consistent for testing unimodal against multimodal distributions. The dip statistic is asymptotically distributed as a Brownian bridge when the data is uniformly distributed. The test is robust to the normality assumption and is not sensitive to the choice of kernel width. The dip test is compared with other tests for multimodality, such as the likelihood ratio test and the depth test, and is found to be more powerful. The dip test is also extended to the multivariate case using the minimum spanning tree. The test is applied to real data, such as the quality of faculty in statistics departments, and is shown to detect multimodality effectively. The dip test is a useful tool for detecting multimodality in data and is recommended for use in statistical analysis.
Reach us at info@study.space
[slides and audio] The Dip Test of Unimodality