Arkiv för Matematik

Convexity of the median in the gamma distribution

Christian Berg and Henrik L. Pedersen

Full-text: Open access

Abstract

We show that the median m(x) in the gamma distribution with parameter x is a strictly convex function on the positive half-line.

Article information

Source
Ark. Mat., Volume 46, Number 1 (2008), 1-6.

Dates
Received: 5 October 2006
Revised: 2 November 2006
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485907017

Digital Object Identifier
doi:10.1007/s11512-006-0037-2

Mathematical Reviews number (MathSciNet)
MR2379680

Zentralblatt MATH identifier
05319828

Rights
2007 © Institut Mittag-Leffler

Citation

Berg, Christian; Pedersen, Henrik L. Convexity of the median in the gamma distribution. Ark. Mat. 46 (2008), no. 1, 1--6. doi:10.1007/s11512-006-0037-2. https://projecteuclid.org/euclid.afm/1485907017


Export citation

References

  • Adell, J. A. and Jodrá, P., Sharp estimates for the median of the Γ(n+1,1) distribution, Statist. Probab. Lett. 71 (2005), 185–191.
  • Alm, S. E., Monotonicity of the difference between median and mean of gamma distributions and of a related Ramanujan sequence, Bernoulli 9 (2003), 351–371.
  • Alzer, H., Proof of the Chen–Rubin conjecture, Proc. Roy. Soc. Edinburgh Sect. A 135 (2005), 677–688.
  • Alzer, H., A convexity property of the median of the gamma distribution, Statist. Probab. Lett. 76 (2006), 1510–1513.
  • Berg, C. and Pedersen, H. L., The Chen–Rubin conjecture in a continuous setting, Methods Appl. Anal. 13 (2006), 63–88.
  • Chen, J. and Rubin, H., Bounds for the difference between median and mean of gamma and Poisson distributions, Statist. Probab. Lett. 4 (1986), 281–283.