Use distribution distance as a likelihood statistic (Anderson-Darling, Wasserstein, Energy)?

[Gabriel-p]

See about using the A-D test as a likelihood. Questions:

1. Is this a valid likelihood?
2. Does it also fit for the number of points?

Also scipy's distances wasserstein_distance, energy_distance can be used

Related:

How to find out if two datasets are close to each other?