I'm just curious and trying to get my head around this question. I feel like this requires applying a probability space structure to the space of all distributions that are not normal, but, I'm thinking maybe someone will have an awesome answer to help me wrap my head around this question.
And I guess I'm deliberately leaving what I mean by "distributions" unspecific here in case someone has some idea like, "if you assume your data is coming from a distribution with a continuous pdf...."