  Consider the random Dirichlet partition of the interval into $n$ fragments
with parameter $\theta >0$. We recall the unordered Ewens sampling formulae
from finite Dirichlet partitions. As this is a key variable for estimation
purposes, focus is on the number of distinct visited species in the sampling
process. These are illustrated in specific cases. We use these preliminary
statistical results on frequencies distribution to address the following
sampling problem: what is the estimated number of species when sampling is from
Dirichlet populations? The obtained results are in accordance with the ones
found in sampling theory from random proportions with Poisson-Dirichlet
distribution. To conclude with, we apply the different estimators suggested to
two different sets of real data.
