  We consider a family of distributions on which natural tail orders can be
constructed upon a representation of a distribution by a (single) hyper-real
number. Past research revealed that the ordering can herein strongly depend on
the particular model of the hyperreals, specifically the underlying
ultrafilter. Hence, our distribution family is constructed to order invariantly
of an ultrafilter. Moreover, we prove that it lies dense in the set of all
distributions with the (same) compact support, w.r.t. the supremum norm.
Overall, this work resents a correction to [10, 12], in response to recent
findings of [2].
