Merging of Linear Combinations to Semistable Laws

Péter Kevei () and Sándor Csörgő ()
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Péter Kevei: University of Szeged
Sándor Csörgő: University of Szeged

Journal of Theoretical Probability, 2009, vol. 22, issue 3, 772-790

Abstract: Abstract 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.

Keywords: Semistable laws; Domains of geometric partial attraction; Merge theorems; Pooling strategies; Linear combinations (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/s10959-007-0138-2

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