The Chen-Rubin conjecture in a continuous setting
Classical Analysis and ODEs
2007-05-23 v1 Complex Variables
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.
Cite
@article{arxiv.math/0411282,
title = {The Chen-Rubin conjecture in a continuous setting},
author = {Henrik L. Pedersen and Christian Berg},
journal= {arXiv preprint arXiv:math/0411282},
year = {2007}
}