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Expressions for the Entropy of Binomial-Type Distributions (1708.06394v4)
Published 21 Aug 2017 in cs.IT, math.IT, math.PR, math.ST, and stat.TH
Abstract: We develop a general method for computing logarithmic and log-gamma expectations of distributions. As a result, we derive series expansions and integral representations of the entropy for several fundamental distributions, including the Poisson, binomial, beta-binomial, negative binomial, and hypergeometric distributions. Our results also establish connections between the entropy functions and to the Riemann zeta function and its generalizations.