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.