Laws of Large Numbers for Asymmetrical Cauchy Random Variables

André Adler

International Journal of Stochastic Analysis, 2007, vol. 2007, 1-6

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.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:056924

DOI: 10.1155/2007/56924

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