Random Scaling of Gumbel Risks

Abstract

In this paper we consider the product of two positive independent risks $Y_1$ and $Y_2$. If $Y_1$ is bounded and $Y_2$ has distribution in the Gumbel max-domain of attraction with some auxiliary function which is regularly varying at infinity, then we show that $Y_1{Y}_2$ has also distribution in the Gumbel max-domain of attraction. Additionally, if both $Y_1,Y_2$ have log-Weibullian or Weibullian tail behavior, we show that $Y_1{Y}_2$ has log-Weibullian or Weibullian asymptotic tail behavior, respectively. We present two applications of our results.

References in corpus (2)

• Asymptotics of Random Contractions
• Asymptotics of supremum distribution of a Gaussian process over a Weibullian time

Cited by in corpus (1)

• Extremes of Aggregated Dirichlet Risks