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\section{Conclusion and Summary}  In our project, we utilize four different test statistics for mode test, three of which are based on GMM. The LRT, bandwidth test, and kurtosis test are derived from the fitted results of GMM by EM algorithm, with the assumption of Gaussianality for all modes. Alternatively, a model-independent method, EMM, is introduced with no need of any prior information for the sample distribution. We generate various mock data in order to test the efficiency and limitation of all the methods and find several interesting results.  If we have no prior information of the shape of sample distribution, it is not a good idea to use GMM-based methods. Although in some cases, GMM-based methods may give reasonable result, most of the time they mislead. A better way is to use EMM to make inference first. Alternatively, if we know the prior information, it is better to put it into LRT in order to make stronger inference than EMM. Kurtosis and D provides an additional checking of bimodality. In easy cases kurtosis < 0 and D>2 D > 2  serve as an additional confirmation of bimodality. However in hard cases kurtosis and D fail to detect bimodality. But they both are still useful to infer overall shape of data - if LRT is big and its p-value < 0.05 and kurtosis and D do not satisfy bimodal distribution, it means that data is biased or peaks are too far.