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Comments on a recent limit theorem of Quine

Author

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  • Galambos, J.
  • Simonelli, I.

Abstract

We give necessary and sufficient conditions for convergence of the self-normalized productwhere X1,X2,...,Xn are independent random variables, g(n) is an arbitrary function with g(n)-->+[infinity], as n-->+ [infinity], and [summation operator] is summation over all integers 1[less-than-or-equals, slant]i1

Suggested Citation

  • Galambos, J. & Simonelli, I., 2003. "Comments on a recent limit theorem of Quine," Statistics & Probability Letters, Elsevier, vol. 63(1), pages 89-95, May.
    • Handle: RePEc:eee:stapro:v:63:y:2003:i:1:p:89-95
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    References listed on IDEAS

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    1. Simonelli, Italo, 2001. "Convergence and symmetry of infinite products of independent random variables," Statistics & Probability Letters, Elsevier, vol. 55(1), pages 45-52, November.
    2. Quine, M. P., 1999. "A central limit theorem for self-normalized products of random variables," Statistics & Probability Letters, Elsevier, vol. 43(2), pages 137-143, June.
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    Cited by:

    1. Novak, S.Y., 2007. "A new characterization of the normal law," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 95-98, January.
    2. Melnykov, Igor & Chen, John T., 2007. "A connection between self-normalized products and stable laws," Statistics & Probability Letters, Elsevier, vol. 77(17), pages 1662-1665, November.

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    1. Melnykov, Igor & Chen, John T., 2007. "A connection between self-normalized products and stable laws," Statistics & Probability Letters, Elsevier, vol. 77(17), pages 1662-1665, November.
    2. Novak, S.Y., 2007. "A new characterization of the normal law," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 95-98, January.

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