Testing for bimodality (created 2005-05-03, updated 2010-07-06)
This page is moving to a new website.
This is an update and revision of age on my old site that has some
broken links:
www.childrensmercy.org/stats/weblog2005/Bimodality.asp.
I have talked about this topic before and it is a rather tricky thing. A recent discussion
of tests of bimodality on edstat-l, though, yielded a few promising leads relating to the Dip
test of
- J. A. Hartigan, P. M. Hartigan. The Dip Test of Unimodality.
The Annals of Statistics. 1985;13(1):70-84. Abstract: "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."
[Accessed July 6, 2010]. Available at:
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aos/1176346577.
-
P. M. Hartigan. Algorithm AS 217: Computation of the Dip Statistic to
Test for Unimodality. Journal of the Royal Statistical Society.
Series C (Applied Statistics). 1985;34(3):320-325. [Accessed July 6,
2010]. Available at:
http://www.jstor.org/stable/2347485.
Some links to software to run the Dip test are shown below.