Open AccessExact Strong Laws for the Range
Author(s) -
André Adler
Publication year - 2020
Publication title -
bulletin of the institute of mathematics academia sinica new series
Language(s) - English
Resource type - Journals
eISSN - 2304-7909
pISSN - 2304-7895
DOI - 10.21915/bimas.2020104
Subject(s) - range (aeronautics) , law , mathematics , political science , engineering , aerospace engineering
In this paper we establish exact strong laws of large numbers for the range of a Pareto random variable. The underlying density is f(x) = xI(x ≥ 1). Neither the first nor second moments of this random variable exist, which makes these theorems unusual. The results are of the form ∑n i=1 aiRi/bn → γ, as n → ∞, where Ri is the range from the i th sample.
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