distinguishing log-concavity from heavy tails
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ID: 260432
2017
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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 X 1 + X 2 occur as result of a single big jump with heavy tails whereas X 1 , X 2 are of equal order of magnitude in the light-tailed case. The method is based on the ratio | X 1 − X 2 | / ( X 1 + X 2 ) , 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.
| Reference Key |
asmussen2017risksdistinguishing
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|---|---|
| Authors | ;Søren Asmussen;Jaakko Lehtomaa |
| Journal | world neurosurgery |
| Year | 2017 |
| DOI |
10.3390/risks5010010
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| URL | |
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