• Bernoulli
  • Volume 20, Number 3 (2014), 1484-1506.

Comparison of multivariate distributions using quantile–quantile plots and related tests

Subhra Sankar Dhar, Biman Chakraborty, and Probal Chaudhuri

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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.

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Bernoulli, Volume 20, Number 3 (2014), 1484-1506.

First available in Project Euclid: 11 June 2014

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characterization of distributions contiguous alternatives Gaussian process Pitman efficacy spatial quantiles tests for distributions the level and the power of test


Dhar, Subhra Sankar; Chakraborty, Biman; Chaudhuri, Probal. Comparison of multivariate distributions using quantile–quantile plots and related tests. Bernoulli 20 (2014), no. 3, 1484--1506. doi:10.3150/13-BEJ530.

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Supplemental materials

  • Supplementary material: Supplement to “Comparison of multivariate distributions using quantile–quantile plots and related tests”. In the supplement, we provide additional multivariate Q–Q plots and discuss the performance of various tests for univariate data.