Correction algorithm for finite sample statistics

Assume in a sample of size M one finds M _i representatives of species i with $i = 1\dots N^{*}$ . The normalized frequency $p^*_i\equiv M_i/M$ , based on the finite sample, may deviate considerably from the true probabilities p _i . We propose a method to infer rank-ordered true probabilities r _i from measured frequencies M _i . We show that the rank-ordered probabilities provide important informations on the system, e.g., the true number of species, the Shannon- and the Renyi-entropies.