Correction algorithm for finite sample statistics
Abstract
Assume in a sample of size M one finds Mi representatives of species i with i=1...N*. The normalized frequency p*i=Mi/M, based on the finite sample, may deviate considerably from the true probabilities pi. We propose a method to infer rank-ordered true probabilities ri from measured frequencies Mi. 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.
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