  We explore the origins of parameters in adimensional theories -- fundamental
theories with no classical massive scales. If the parameters originate as draws
from a distribution, it should be possible to write a distribution for them
that doesn't depend on or introduce any massive scales. These distributions are
the invariant distributions for the renormalization group (RG). If there exist
RG invariant combinations of parameters, the RG invariant distributions are
specified up to arbitrary functions of the RG invariants. If such distributions
can be constructed, adimensional theories could predict the values of their
parameters through distributions that are constrained by the RG. If they can't
be constructed, the parameters must originate in a different way. We
demonstrate the RG invariant distributions in QCD, the Coleman-Weinberg model
and a totally asymptotically free theory.
