On Max-Multiscaling Distributions as Extended Max-Semistable Ones

Abstract

We introduce max-multiscaling distributions as solutions to a functional equation which, in a natural way, extends the one fulfilled by max-semistable distributions. We establish that strictly max-multiscaling distributions are products of at most two max-semistable distributions. Next, we show how to obtain these solutions as limit laws of normalized maximum of suitable independent sequences of random variables when sample size has geometric growth.

Key Words:

• Max-stability
• Max-semistability
• Choquet–Deny functional equation
• Limit laws

AMS Classification:

• 60E05
• 60E07
• 60G70
• 60G18
• 60G52
• 60F05

Acknowledgment

The authors feel indebted to their referees who contributed in improving an early version of this draft.