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Laws of Large Numbers for Asymmetrical Cauchy Random Variables

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  • André Adler

Abstract

We generalize the Cauchy distribution so that we can have asymmetrical tails. This allows us to obtain unusual laws of large numbers involving weighted sums of these random variables. Unusual in the sense that even though in every case E | X | = ∞ , we can still obtain a nonzero limit for these weighted sums.

Suggested Citation

  • André Adler, 2007. "Laws of Large Numbers for Asymmetrical Cauchy Random Variables," International Journal of Stochastic Analysis, Hindawi, vol. 2007, pages 1-6, January.
    • Handle: RePEc:hin:jnijsa:056924
    DOI: 10.1155/2007/56924
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    Cited by:

    1. Rita Giuliano & Milto Hadjikyriakou, 2021. "On Exact Laws of Large Numbers for Oppenheim Expansions with Infinite Mean," Journal of Theoretical Probability, Springer, vol. 34(3), pages 1579-1606, September.

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