# Significance of modes in a distribution

I have several datasets with angular measurements, i.e. circular values from 0 to $$2\pi$$. These datasets tend to have peaks at 0 and/or $$\pi$$, and I need to tell if the peaks are detected/significant. There are several approaches to related problems I found, but they don't seem to answer the question of individual peak (mode) significance:

• Fitting a mixture model with a uniform component + 2 gaussians at 0 and $$\pi$$, and getting the posterior for the parameters. The posterior means for weights of each component are basically always distinct from zero , even when fitting to a uniform distribution. So this cannot be used to assess peak significance.
• Different multimodality tests: only test for the number of modes, and don't give their locations.

So I'm looking for help and suggestions - what are better ways to do this?

• Since you want to perform a hypothesis test, can you say more specifically what your null hypothesis is? – user20160 Jul 18 '19 at 13:24
• @user20160 there is not a single hypothesis to test here, but a combination of two: "is there a mode at 0" and "is there a mode at pi". Corresponding null hypotheses are that the distribution has no mode at those locations. – aplavin Jul 18 '19 at 13:38