Laws of Large Numbers for Asymmetrical Cauchy Random Variables

[摘要] We generalize the Cauchy distribution so that we can have asymmetricaltails. 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 caseE|X|=∞, we can still obtain a nonzero limit for these weighted sums.

[学科分类] 应用数学