Guessing probability distributions from small samples

Abstract

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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References in corpus (2)

• Entropy and Long range correlations in literary English
• Entropy and Long range correlations in literary English

Cited by in corpus (3)

• A Statistical Measure of Complexity
• Entropy estimates of small data sets
• Finite-sample frequency distributions originating from an equiprobability distribution