ISSN:
1572-9052
Keywords:
Bernstein function
;
Laplace-Stieltjes transform
;
infinite divisibility
;
geometric infinite divisibility
;
Lévy process
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In a recent article Pillai (1990,Ann. Inst. Statist. Math.,42, 157–161) showed that the distribution 1−E α(−x α), 0〈α≤1; 0≤x, whereE α(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, ∞).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00775821
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