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Correction algorithm for finite sample statistics

Thorsten Poeschel·Werner Ebeling·Cornelius Froemmel·Rosa Ramirez
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Abstract

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.

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Thorsten Poeschel, Werner Ebeling, Cornelius Froemmel, Rosa Ramirez. 2004-01-28. Correction algorithm for finite sample statistics. https://arxiv.org/abs/q-bio/0401040

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