[R] Plotting Bivariate Normal Data

Martin Maechler maechler at stat.math.ethz.ch
Mon Oct 25 08:43:12 CEST 2004

>>>>> "JohnF" == John Fox <jfox at mcmaster.ca>
>>>>>     on Sun, 24 Oct 2004 12:37:09 -0400 writes:

    JohnF> Dear Sarah, If the data are allegedly bivariate
    JohnF> normal, then they are probably two vectors, not
    JohnF> one. Assuming that this is the case, I know of
    JohnF> nothing quite as neat as a univariate QQ plot to
    JohnF> check visually for bivariate normality (perhaps
    JohnF> someone else has a suggestion here), but you could
    JohnF> superimpose bivariate-normal contours on a
    JohnF> scatterplot of the data, perhaps along with a
    JohnF> bivariate density estimate. The car and ellipse
    JohnF> packages can do the former, while the locfit and sm
    JohnF> packages (and possibly others) can do the latter.

Since one of the more severe and common deviations from
normality is "long tailed"ness (in all it's vaguety), we have
been recommending to QQ-plot mahalanobis distances against chi
squared quantiles - even before looking at the univariate
QQ plots.

Exactly for this reason, in R,
shows a version of how to do this!

Martin Maechler, ETH Zurich

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