  A predictive distribution over a sequence of $N+1$ events is said to be
"frequency mimicking" whenever the probability for the final event conditioned
on the outcome of the first $N$ events equals the relative frequency of
successes among them. Infinitely extendible exchangeable distributions that
universally inhere this property are known to have several annoying concomitant
properties. We motivate frequency mimicking assertions over a limited subdomain
in practical problems of finite inference, and we identify their computable
coherent implications. We provide some computed examples using reference
distributions, and we introduce computational software to generate any
specification. The software derives from an inversion of the finite form of the
exchangeability representation theorem. Three new theorems delineate the extent
of the usefulness of such distributions, and we show why it may not be
appropriate to extend the frequency mimicking assertions for a specified value
of $N$ to any arbitrary larger size of $N$. The constructive results identify
the source and structure of "adherent masses" in the limit of a sequence of
finitely additive distributions. Appendices develop a novel geometrical
representation of conditional probabilities which illuminate the analysis.
