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Guessing probability distributions from small samples

: Pöschel, T.; Ebeling, W.; Rose, H.


Journal of statistical physics 80 (1995), Nr.5-6, S.1443-1452
ISSN: 0022-4715
Fraunhofer FIRST ()

We propose a new method for the calculation of the statistical properties, as e.g. the entropy, of unknown generators of symbolic sequences. The probability distribution p(k) of the elements k of a population can be approximated by the frequencies f(k) of a sample provided the sample is long enough so that each element k occurs many times. Our method yields an approximation if this precondition does not hold. For a given f(k) we recalculate the Zipf-ordered probability distribution by optimization of the parameters of a guessed distribution. We demonstrate that our method yields reliable results.