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A generalization of the results of Pillai (1993)

Fujita, Yasuhiro

Springer

Annals of the Institute of Statistical Mathematics 45 (1993), S. 361-365

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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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