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Wikipedia gives the following formula for normal distributions:

What changes, if any, do I need to make to handle multivariate lognormal distributions instead?

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    $\begingroup$ The Wasserstein distance is parameterisation dependent, so it will differ for log-normal distributions $\endgroup$
    – Xi'an
    Commented Jun 1, 2022 at 7:02
  • $\begingroup$ 1) Is that formula correct? It is not in the paper cited by the Wikipedia article, since that paper considers only normal distributions with 0 mean. 2) The phrase "Wasserstein distance" in the title suggests the usual Wasserstein 1-distance, but the formula is for the 2-distance. So it would be better for the title to refer to "Wasserstein 2-distance", or for the formula to be omitted, or (depending on what you want) just to ask for any theoretically-grounded distance with an explicit formula. $\endgroup$
    – user225256
    Commented Jun 6, 2022 at 14:39

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