Random Scaling of Gumbel Risks

2013/12/26 by Dȩbicki, Krzysztof, Farkas, Julia, Hashorva, Enkelejd
#Applications (stat.AP) #FOS: Computer and information sciences #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1312.7132

Abstract

In this paper we consider the product of two positive independent risks Y₁ and Y₂. If Y₁ is bounded and Y₂ has distribution in the Gumbel max-domain of attraction with some auxiliary function which is regularly varying at infinity, then we show that Y₁Y₂ has also distribution in the Gumbel max-domain of attraction. Additionally, if both Y₁,Y₂ have log-Weibullian or Weibullian tail behavior, we show that Y₁Y₂ has log-Weibullian or Weibullian asymptotic tail behavior, respectively. We present two applications of our results.

Related

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