I have a handful of 1D distributions that I built using Kernel Density Estimation with Gaussian Kernels. Most of the distribution are multimodal. I want to rank them according to the dispersion of each distribution, but I want to capture intra-cluster (or intra-mode) dispersion, disregarding how far apart are each mode is from the others.
Standard deviation and the like do not seem reasonable to apply as they will largely affected by the distance between modes and not the dispersion of the points clustered around them.
I am thinking of estimating a "local" standard deviation where I measure the average distance to the closest local maxima (or mode). But before doing that (and probably reinventing the wheel)... is there some well-known dispersion metric that measures that?
Note: I would like to avoid any preliminary step involving clustering or fitting a mixture or Gaussian or the like, as I do not want to carry errors in that step further down the pipeline.