Distinguishing Log-Concavity from Heavy Tails
Department of Mathematics, Aarhus University, Ny Munkegade 118, DK-8000 Aarhus C, Denmark
Author to whom correspondence should be addressed.
Academic Editor: Qihe Tang
Received: 14 November 2016 / Revised: 10 January 2017 / Accepted: 17 January 2017 / Published: 7 February 2017
Well-behaved densities are typically log-convex with heavy tails and log-concave with light ones. We discuss a benchmark for distinguishing between the two cases, based on the observation that large values of a sum
occur as result of a single big jump with heavy tails whereas
are of equal order of magnitude in the light-tailed case. The method is based on the ratio
, for which sharp asymptotic results are presented as well as a visual tool for distinguishing between the two cases. The study supplements modern non-parametric density estimation methods where log-concavity plays a main role, as well as heavy-tailed diagnostics such as the mean excess plot.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
Scifeed alert for new publications
Never miss any articles
matching your research from any publisher
- Get alerts for new papers matching your research
- Find out the new papers from selected authors
- Updated daily for 49'000+ journals and 6000+ publishers
Define your Scifeed now
Share & Cite This Article
MDPI and ACS Style
Asmussen, S.; Lehtomaa, J. Distinguishing Log-Concavity from Heavy Tails. Risks 2017, 5, 10.
Asmussen S, Lehtomaa J. Distinguishing Log-Concavity from Heavy Tails. Risks. 2017; 5(1):10.
Asmussen, Søren; Lehtomaa, Jaakko. 2017. "Distinguishing Log-Concavity from Heavy Tails." Risks 5, no. 1: 10.
Show more citation formats
Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
[Return to top]
Multiple requests from the same IP address are counted as one view.