Geometrically Strictly Semistable Laws as the Limit Laws
نویسندگان
چکیده
A random variableX is geometrically infinitely divisible iff for every p ∈ (0, 1) there exists random variable Xp such that X d = ∑T (p) k=1 Xp,k, where Xp,k’s are i.i.d. copies of Xp, and random variable T (p) independent of {Xp,1, Xp,2, . . .} has geometric distribution with the parameter p. In the paper we give some new characterization of geometrically infinitely divisible distribution. The main results concern geometrically strictly semistable distributions which form a subset of geometrically infinitely divisible distributions. We show that they are limit laws for random and deterministic sums of independent random variables.
منابع مشابه
On Some Limit Distributions for Geometric Random Sums
We define and give the various characterizations of a new subclass of geometrically infinitely divisible random variables. This subclass, called geometrically semistable, is given as the set of all these random variables which are the limits in distribution of geometric, weighted and shifted random sums. Introduced class is the extension of, considered until now, classes of geometrically stable...
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