TY - JOUR
T1 - A generalization of the results of Pillai
AU - Fujita, Yasuhiro
PY - 1993/6
Y1 - 1993/6
N2 - In a recent article Pillai (1990, Ann. Inst. Statist. Math., 42, 157-161) showed that the distribution 1-Eα(-xα), 0<α≤1; 0≤x, where Eα(x) is the Mittag-Leffler function, is infinitely divisible and geometrically infinitely divisible. He also clarified the relation between this distribution and a stable distribution. In the present paper, we generalize his results by using Bernstein functions. In statistics, this generalization is important, because it gives a new characterization of geometrically infinitely divisible distributions with support in (0, ∞).
AB - In a recent article Pillai (1990, Ann. Inst. Statist. Math., 42, 157-161) showed that the distribution 1-Eα(-xα), 0<α≤1; 0≤x, where Eα(x) is the Mittag-Leffler function, is infinitely divisible and geometrically infinitely divisible. He also clarified the relation between this distribution and a stable distribution. In the present paper, we generalize his results by using Bernstein functions. In statistics, this generalization is important, because it gives a new characterization of geometrically infinitely divisible distributions with support in (0, ∞).
KW - Bernstein function
KW - Laplace-Stieltjes transform
KW - Lévy process
KW - geometric infinite divisibility
KW - infinite divisibility
UR - http://www.scopus.com/inward/record.url?scp=0040708384&partnerID=8YFLogxK
U2 - 10.1007/BF00775821
DO - 10.1007/BF00775821
M3 - 学術論文
AN - SCOPUS:0040708384
SN - 0020-3157
VL - 45
SP - 361
EP - 365
JO - Annals of the Institute of Statistical Mathematics
JF - Annals of the Institute of Statistical Mathematics
IS - 2
ER -