A Generalization of the Results of Pillai
نویسنده
چکیده
In a recent article Pillai (1990, Ann. Inst. Statist. Math., 42, 157-161) showed that the distribution 1-E~(-x~), 0 < c~ _< 1; 0 _< x, where E~(x) is the Mittag-Lettter 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, c~).
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تاریخ انتشار 2004