A notion of data depth has been used for multivariate data analysis. It is found to be useful for testing location/scale parameters, the goodness of fit tests, classification, clustering, etc. Recently, the concept of depth has been extended to functional data and it has attracted a lot of attention among researchers. In the present paper, we discuss the graphical tool for comparing two functional populations. Based on the graphical tool, we propose the tests for equality of mean functions, the test for the equality of covariance functions, and the tests for homogeneity of two functional populations. A simulation study is performed to assess the performance of the proposed test. A simulation study has revealed that the proposed tests are performing better than the existing tests considered here. Finally, graphical tool and proposed tests are applied to analyze several real datasets.
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