Limit laws of modulus trimmed sums

Philip S. Griffin, Fozia S. Qazi

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

Let X, X1, X2,... be a sequence of independent and identically distributed random variables. Let (1)Xn,...,(n)Xn be an arrangement of X1, X2,...,Xn in decreasing order of magnitude, and set (rn)Sn = (rn+1)Xn +···+(n)Xn. This is known as the modulus trimmed sum. We obtain a complete characterization of the class of limit laws of the normalized modulus trimmed sum when the underlying distribution is symmetric and rn → ∞, rnn-1 → 0.

Original languageEnglish (US)
Pages (from-to)1466-1485
Number of pages20
JournalAnnals of Probability
Volume30
Issue number3
DOIs
StatePublished - Jul 1 2002

Keywords

  • Limit laws
  • Stable laws
  • Trimmed sum

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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