Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/167911
Authors: 
Asmussen, Søren
Lehtomaa, Jaakko
Year of Publication: 
2017
Citation: 
[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 5 [Year:] 2017 [Issue:] 1 [Pages:] 1-14
Abstract: 
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 X1 + X2 occur as result of a single big jump with heavy tails whereas X1,X2 are of equal order of magnitude in the light-tailed case. The method is based on the ratio X1 - X2/(X1 + X2 ), 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.
Subjects: 
heavy-tailed
log-concave
mean excess function
principle of a single big jump
Persistent Identifier of the first edition: 
Creative Commons License: 
http://creativecommons.org/licenses/by/4.0/
Document Type: 
Article
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