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.
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机译：我们推广柯西分布，这样我们就可以拥有不对称的尾巴。这使我们能够获得涉及这些随机变量的加权和的大量异常定律。即使在每种情况下E | X | =∞，我们仍然可以获得这些加权和的非零极限。
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