deletions | additions       diff --git a/GMM.tex b/GMM.tex  index eea1b12..8e0727b 100644  --- a/GMM.tex  +++ b/GMM.tex 
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Conclusion about data is made based on 3 parameters:  1. LRT (Likelihood ratio test)  $-2 \ln \lambda = 2[\ln L_{bimodal} - \ln L_{unimodal}] \sim \chi^2$ ( $-2 \ln \lambda$ is the main parameter for making conclusion about bimodality of data. The bigger $-2 \ln \lambda$ is, the more we are convinced that distribution is bimodal). 2. (Bandwidth test)  $D = \frac {|\mu_1 - \mu_2|}{(\sigma^2_1+\sigma^2_2)/2)^{0.5}}$ ($D (distance)  > 2$ is necessary for a clear separation of 2 peaks). 3. (Kurtosis test)  $kurtosis < 0$ should be negative for a bimodal distribution. In some hard cases $D$ and $kurtosis$ fail to detect bimodality:  \begin{tabular}{l l}  \begin{minipage}{0.5\textwidth}  {\tt  dd  \end{minipage}  &  \begin{minipage}{0.5\textwidth}  d  \end{minipage}