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  • Limit theorems for triangular arrays under a relaxed asymptotic negligibility condition

  • Part of
  • Miloslav Jirina
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 42 / Issue 1 / February 1987
    Published online by Cambridge University Press:
    09 April 2009, pp. 117-128
    Print publication:
    February 1987
    • Article
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  • Let {Xnk} be a triangular array of independent random variables satisfying the so-called tail-negligibility condition, i.e. such that Prob{|Xnk| > a} → 0 as both k, n → ∞. It is also assumed that for each fixed k, Xnk converges in distribution as n → ∞. Theorems on the asymptotic behavior of the row sums of the array, analogous to those of the classical theory under the uniform negligibility condition, are presented.