Guessing probability distributions from small samples

Details Guessing probability distributions from small samples Guessing probability distributions from small samples

2002-03-22

arxiv.org/abs/cond-mat/0203467v1

J. Stat. Phys., Vol. 80, 1443 (1995)

Physics

Condensed Matter

Statistical Mechanics

10 pages, 5 figures

Scientific paper

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.

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