It looked misleading to me because from the histogram it's not visible from where the two bumps in the left distribution come from. With the x histogram is clearer that the oversmoothing matches the two groups of sample points.

When I run your example with the 4000 points (which is slow) it shows that the corrected rules of thumb still oversmooth, as expected for mixtures.

I sent a plot to the mailing list that has only 0.05 weight on the lower, left mixture to be closer to the normal reference case.

you could get the true pdf from 
`pdf(x) = 0.25 * stats.norm.pdf(x_grid, loc=loc1, scale=scale1) + 0.75 * stats.norm.pdf(x_grid, loc=loc1, scale=scale2)`
using `from scipy import stats`

I thought we added the pdf to the mixture in statsmodels.distributions, maybe not.


(Otherwise, I'm to exhausted today to think about, or review details.)