Max-Geometric infinite divisibility and stability

S. T. Rachev, S. Resnick

Research output: Contribution to journalArticle

18 Scopus citations

Abstract

We consider a stability property for Rd-valued random vectors appropriate for describing extreme events up to the time of a catastrophe. Let N(p) be geometrically distributed. The random vector Y is max-geometrically infinitely divisible if for some iid random vectors {Yp,j, j≥ 1 independent of N(p) we have [formula ommitted], for any 0 < p < 1. is max-geometrically stable if for 0 < p < 1, for Y, Yn, n ≥ 1 iid and independent of N(p), we have Y and [formula ommitted] Yj of the same type. These distributions are characterized and domains of attraction and related rates of convergence questions explored.

Original languageEnglish
Pages (from-to)191-218
Number of pages28
JournalCommunications in Statistics. Stochastic Models
Volume7
Issue number2
DOIs
StatePublished - Jan 1 1991

    Fingerprint

Cite this