Limit distributions for products of sums

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Abstract

Let {X,Xn, n ≥ 1} be a sequence of independent and identically distributed positive random variables and set Sn = ∑j=1n for n ≥ 1. This paper proves that properly normalized products of the partial sums, (∏j=1n Sj/n!μn)μ/An, converges in distribution to some nondegenerate distribution when X is in the domain of attraction of a stable law with index α ∈ (1,2].

Original languageEnglish (US)
Pages (from-to)93-100
Number of pages8
JournalStatistics and Probability Letters
Volume62
Issue number1
DOIs
StatePublished - Mar 15 2003

Keywords

  • Limit distribution
  • Product of sums
  • Stable laws

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