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Merging of Linear Combinations to Semistable Laws

Author

Listed:
  • Péter Kevei

    (University of Szeged)

  • Sándor Csörgő

    (University of Szeged)

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.

Suggested Citation

  • Péter Kevei & Sándor Csörgő, 2009. "Merging of Linear Combinations to Semistable Laws," Journal of Theoretical Probability, Springer, vol. 22(3), pages 772-790, September.
    • Handle: RePEc:spr:jotpro:v:22:y:2009:i:3:d:10.1007_s10959-007-0138-2
    DOI: 10.1007/s10959-007-0138-2
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    References listed on IDEAS

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    1. Kevei, Péter, 2007. "Generalized n-Paul paradox," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1043-1049, June.
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    Cited by:

    1. Péter Kevei & Dalia Terhesiu, 2022. "Strong Renewal Theorem and Local Limit Theorem in the Absence of Regular Variation," Journal of Theoretical Probability, Springer, vol. 35(2), pages 1013-1048, June.
    2. Péter Kevei & Dalia Terhesiu, 2020. "Darling–Kac Theorem for Renewal Shifts in the Absence of Regular Variation," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2027-2060, December.

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