Guessing probability distributions from small samples

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

1995-04-04

arxiv.org/abs/chao-dyn/9504003v1

Nonlinear Sciences

Chaotic Dynamics

10 pages, uuencoded compressed PostScript

Scientific paper

10.1007/BF02179880

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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