Complete monotonicity of the entropy in the central limit theorem for gamma and inverse Gaussian distributions

Yaming Yu

Statistics & Probability Letters, 2009, vol. 79, issue 2, 270-274

Abstract: Let Hg([alpha]) be the differential entropy of the gamma distribution Gam. It is shown that (1/2)log(2[pi]e)-Hg([alpha]) is a completely monotone function of [alpha]. This refines the monotonicity of the entropy in the central limit theorem for gamma random variables. A similar result holds for the inverse Gaussian family. How generally this complete monotonicity holds is left as an open problem.

Date: 2009
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