Distinguishing Log-Concavity from Heavy Tails
نویسندگان
چکیده
منابع مشابه
Distinguishing Log-Concavity from Heavy Tails
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 ...
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This is a small observation concerning scale mixtures and their log-concavity. A function f(x) ≥ 0, x ∈ Rn is called log-concave if f (λx + (1− λ)y) ≥ f(x)f(y) (1) for all x,y ∈ Rn, λ ∈ [0, 1]. Log-concavity is important in applied Bayesian Statistics, since a distribution with a log-concave density is easy to treat with many different approximate inference techniques. For example, log-concavit...
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ژورنال
عنوان ژورنال: Risks
سال: 2017
ISSN: 2227-9091
DOI: 10.3390/risks5010010