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 PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Berg, C., Pedersen, H. Convexity of the median in the gamma distribution. Ark Mat 46, 1–6 (2008). https://doi.org/10.1007/s11512-006-0037-2
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11512-006-0037-2