  Large sample size equivalence between the celebrated {\it approximated}
Good-Turing estimator of the probability to discover a species already observed
a certain number of times (Good, 1953) and the modern Bayesian nonparametric
counterpart has been recently established by virtue of a particular smoothing
rule based on the two-parameter Poisson-Dirichlet model. Here we improve on
this result showing that, for any finite sample size, when the population
frequencies are assumed to be selected from a superpopulation with
two-parameter Poisson-Dirichlet distribution, then Bayesian nonparametric
estimation of the discovery probabilities corresponds to Good-Turing {\it
exact} estimation. Moreover under general superpopulation hypothesis the
Good-Turing solution admits an interpretation as a modern Bayesian
nonparametric estimator under partial information.
