Correction algorithm for finite sample statistics

Poeschel, Thorsten; Ebeling, Werner; Froemmel, Cornelius; Ramirez, Rosa

Correction algorithm for finite sample statistics

Authors

Description

Assume in a sample of size M one finds M_i representatives of species i with i=1...N^*. The normalized frequency p^*_i=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.
11 pages, 9 figures