The Chen-Rubin conjecture in a continuous setting

Details The Chen-Rubin conjecture in a continuous setting The Chen-Rubin conjecture in a continuous setting

2004-11-12

arxiv.org/abs/math/0411282v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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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