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 -