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The Chen-Rubin conjecture in a continuous setting

Henrik L. Pedersen·Christian Berg
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Abstract

We study the median in the Gamma distribution as a function of the parameter. Using methods from complex analysis we show that the derivative of the median is less than 1 and we thereby solve a conjecture of Chen and Rubin from 1986. We also study the asymptotic behaviour of the median at infinity and at zero.

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Henrik L. Pedersen, Christian Berg. 2004-11-12. The Chen-Rubin conjecture in a continuous setting. https://arxiv.org/abs/math/0411282

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