THE CHEN-RUBIN CONJECTURE IN A CONTINUOUS SETTING

摘要

We study the median m(x) in the gamma distribution with parameter x and show that 0 < m'(x) < ] for all x > 0. This proves a generalization of a conjecture of Chen and Rubin from 1986: The sequence m(n) -n decreases for n > 1. We also describe the asymptotic behaviour of in and m' at zero and at infinity.