  The univariate quantile-quantile (Q-Q) plot is a well-known graphical tool
for examining whether two data sets are generated from the same distribution or
not. It is also used to determine how well a specified probability distribution
fits a given sample. In this article, we develop and study a multivariate
version of the Q-Q plot based on the spatial quantile. The usefulness of the
proposed graphical device is illustrated on different real and simulated data,
some of which have fairly large dimensions. We also develop certain statistical
tests that are related to the proposed multivariate Q-Q plot and study their
asymptotic properties. The performance of those tests are compared with that of
some other well-known tests for multivariate distributions available in the
literature.
