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Abstract:
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We consider the within and between interpoint distances (IPDs) of two groups of observations in $\mathbb{R}^d$. We suggest a simultaneous plot of the empirical cumulative distribution functions of the IPDs to visualize and examine the equality of the underlying distribution functions of the observations. We provide several examples to illustrate how such plots can be utilized to envision and canvass the relationship between the two distributions under location shift, scale, shape, and dependence changes. We extend the simultaneous plots to compare $k>2$ distributions and suggest new statistics for testing the equality of $k$ distributions. We compare the new statistics to existing test statistics based on the IPDs under changes in location and scale.
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