The Chen-Rubin Conjecture in a Continuous Setting
@article{Berg2004TheCC, title={The Chen-Rubin Conjecture in a Continuous Setting}, author={H. Berg}, journal={Methods and applications of analysis}, year={2004}, volume={13}, pages={63-88} }
We study the median m(x) in the gamma distribution with parameter x and show that 0 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 m and m 0 at zero and at infinity.
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References
SHOWING 1-10 OF 26 REFERENCES
Monotonicity of the difference between median and mean of gamma distributions and of a related Ramanujan sequence
- Mathematics
- 2003
- 23
- PDF
Bounds for the difference between median and mean of gamma and poisson distributions
- Mathematics
- 1986
- 51
The problems submitted by Ramanujan to the Journal of the Indian Mathematical Society [ MR1665361 (2000i:11003)]
- Philosophy, Mathematics
- 2001
- 21
- PDF