Iterated logarithm inequalities.
D. A. Darling,Herbert Robbins +1 more
TLDR
A sequence of independent, identically distributed random variables with mean 0, variance 1, and moment generating function ϕ(t) = E(etz) finite in some neighborhood of t= 0 is introduced.Abstract:
1. Introduction—Let x,x 1, x 2 … be a sequence of independent, identically distributed random variables with mean 0, variance 1, and moment generating function ϕ(t) = E(etz) finite in some neighborhood of t= 0, and put S n = x 1, + … + x n, \(\bar x\) n = S n/n. For any sequence of positive constants a n, n ≥ 1, let P m = P(|\(\bar x\) n| ≥ a n for some n ≥ m).read more
Citations
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References
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TL;DR: In this paper, the Koopman-Darmois family of generalized probability density functions on the measure space has been studied and the main result of Theorem 1 is proved by constructing bounded length confidence intervals.
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