  Gibbs-type random probability measures and the exchangeable random partitions
they induce represent an important framework both from a theoretical and
applied point of view. In the present paper, motivated by species sampling
problems, we investigate some properties concerning the conditional
distribution of the number of blocks with a certain frequency generated by
Gibbs-type random partitions. The general results are then specialized to three
noteworthy examples yielding completely explicit expressions of their
distributions, moments and asymptotic behaviors. Such expressions can be
interpreted as Bayesian nonparametric estimators of the rare species variety
and their performance is tested on some real genomic data.
