From light tails to heavy tails through multiplier

From light tails to heavy tails through multiplier

Let X and Y be two independent nonnegative random variables, of which X has a distribution belonging to the class L(γ ) or S(γ ) for some γ ≥ 0 and Y is unbounded. We study how their product XY inherits the tail behavior of X. Under some mild technical assumptions we prove that the distribution of XY belongs to the class L(0) or S(0) accordingly. Hence, the multiplier Y builds a bridge between ...

Heavy Tails of Ols

Suppose the tails of the noise distribution in a regression exhibit power law behavior. Then the distribution of the OLS regression estimator inherits this tail behavior. This is relevant for regressions involving …nancial data. We derive explicit …nite sample expressions for the tail probabilities of the distribution of the OLS estimator. These are useful for inference. Simulations for medium ...

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 ...

A Practical Guide to Heavy Tails

Variable heavy tails in Internet traffic

This paper studies tails of the size distribution of Internet data flows and their “heaviness”. Data analysis motivates the concepts of moderate, far and extreme tails for understanding the richness of information available in the data. The data analysis also motivates a notion of “variable tail index”, which leads to a generalization of existing theory for heavy-tail durations leading to long-...