I'm a programmer, not a math guy, so please answer in English. ;)
Suppose I have a multi-modal univariate distribution like:
.. . .. ........... .. . .. .
but with each "cluster" (where each clusters is normally distributed) much further apart and more clusters. If I do a density plot of this with R, it's going to be spiky, but some of the less dense spikes might not be smooth because the "optimal" bandwidth was dominated by the more dense clusters.
Compare to a unimodal distribution like:
. . . .. . . . ... .. . . .. . . . .
The density plot of this distribution would look just fine.
What property describes the multi-modality of a distribution? I'm pretty sure that the former distribution would be better modeled by separating each cluster into a separate distribution and doing a density plot on it separately. But I'm unsure how to separate the distribution into these clusters robustly.