is to use the Rosenblatt transformation which is a diffeomorphism from into the standard space , where distributions are normal, with zero mean, unit variance and unit correlation matrix (which is equivalent in that normal case to independent components).
The cumulative distribution function of the conditional variable is defined by:
Rosenblatt transformation: Let in be a continuous random vector defined by its marginal cumulative distribution functions and its copula . The Rosenblatt transformation of is defined by:
where both transformations , and are given by:
See the available Rosenblatt transformations.
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Rosenblatt, “Remarks on a Multivariat Transformation”, The Annals of Mathematical Statistics, Vol. 23, No 3, pp. 470-472.