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3. (Kurtosis test) $kurtosis < 0$ should be negative for a bimodal distribution.  In some hard cases $D$ and $kurtosis$ fail to detect bimodality. That is why our main test is LRT.  For example on the next 2 plots distributions are bimodal, however on 1 plot D<2 (it is hard to distinguish 2 peaks) and on the 2 plot kurtosis is positive and that corresponds to unimodal distribution (it happens because distribution is biased):