Graphical Comparison of High‐Dimensional Distributions

Summary We consider groups of observations in and present a simultaneous plot of the empirical cumulative distribution functions of the within and between interpoint distances to visualise and examine the equality of the underlying distribution functions of the observations. We provide several examples to illustrate how such plots can be utilised to envision and canvass the relationship between the two distributions under location, scale, dependence and shape changes. We suggest new statistics for testing the equality of distributions and extend the simultaneous plots to visualise them. We compare the new statistics to existing tests based on the interpoint distances.