TY - JOUR

T1 - Max-Geometric infinite divisibility and stability

AU - Rachev, S. T.

AU - Resnick, S.

N1 - Funding Information:
Grant MCS-881034 and by Cornell's
Funding Information:
*TWO visits to Cornell were supported by Cornell's Mathematical Sciences Institute and by Cornell's Center for Applied Mathematics as part of the Special Focus on Extremes, Stable Processes and Heavy Tailed Phenomena. The first author gratefully acknowledges this
Funding Information:
support. * * Partially supported by NSF

PY - 1991

Y1 - 1991

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0000762355&partnerID=8YFLogxK

U2 - 10.1080/15326349108807184

DO - 10.1080/15326349108807184

M3 - Article

AN - SCOPUS:0000762355

SN - 0882-0287

VL - 7

SP - 191

EP - 218

JO - Communications in Statistics. Part C: Stochastic Models

JF - Communications in Statistics. Part C: Stochastic Models

IS - 2

ER -