An improved estimate of the inverse binary entropy function

05/05/2020

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by   Reginald D. Smith, et al.

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Two estimates for the inverse binary entropy function are derived using the property of information entropy to estimate combinatorics of sequences as well as related formulas from population genetics for the effective number of alleles. The second estimate shows close correspondence to the actual value of the inverse binary entropy function and can be seen as a close approximation away from low values of binary entropy where p or 1-p are small.