Abstract.
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.
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Received: 14 July 2003, Published online: 5 February 2004
PACS:
02.50.-r Probability theory, stochastic processes, and statistics - 02.60.-x Numerical approximation and analysis - 07.05.Kf Data analysis: algorithms and implementation; data management
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Pöschel, T., Ebeling, W., Frömmel, C. et al. Correction algorithm for finite sample statistics. Eur. Phys. J. E 12, 531–541 (2003). https://doi.org/10.1140/epje/e2004-00025-4
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DOI: https://doi.org/10.1140/epje/e2004-00025-4