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Zbl 1173.60306
Kevei, Péter; Csörgö, Sándor
Merging of linear combinations to semistable laws. (English)
[J] J. Theor. Probab. 22, No. 3, 772-790 (2009). ISSN 0894-9840; ISSN 1572-9230/e

Summary: We prove merge theorems along the entire sequence of natural numbers for the distribution functions of suitably centered and normed linear combinations of independent and identically distributed random variables from the domain of geometric partial attraction of any non-normal semistable law. Surprisingly, for some sequences of linear combinations, not too far from those with equal weights, the merge theorems reduce to ordinary asymptotic distributions with semistable limits. The proofs require working out general conditions for merging in terms of characteristic functions.

MSC 2000:: *60E07 Infinitely divisible distributions
60E05 General theory of probability distributions
60E10 Transforms of probability distributions
60F05 Weak limit theorems

Keywords: semistable laws; domains of geometric partial attraction; merge theorems; pooling strategies; linear combinations

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