MD isn't defined over distributions, though. There are perfectly good distance metrics defined over distributions, but MD isn't one of them. It's a "distance" b

MD isn't defined over distributions, though. There are perfectly good distance metrics defined over distributions, but MD isn't one of them. It's a "distance" between one distribution and one point, not between two distributions or two points. Mahalanobis "distance" is more closely related to a likelihood function than to a true distance function.