The univariate quantile-quantile (Q-Q) plot is a well-known graphical toolfor examining whether two data sets are generated from the same distribution ornot. It is also used to determine how well a specified probability distributionfits a given sample. In this article, we develop and study a multivariateversion of the Q-Q plot based on the spatial quantile. The usefulness of theproposed graphical device is illustrated on different real and simulated data,some of which have fairly large dimensions. We also develop certain statisticaltests that are related to the proposed multivariate Q-Q plot and study theirasymptotic properties. The performance of those tests are compared with that ofsome other well-known tests for multivariate distributions available in theliterature.
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