Open AccessLaws of Large Numbers for Asymmetrical Cauchy Random Variables
Author(s) -
André Adler
Publication year - 2007
Publication title -
journal of applied mathematics and stochastic analysis
Language(s) - English
Resource type - Journals
eISSN - 1687-2177
pISSN - 1048-9533
DOI - 10.1155/2007/56924
Subject(s) - cauchy distribution , mathematics , algorithm , limit (mathematics) , distribution (mathematics) , statistics , mathematical analysis
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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