Some Results on Small-Deviation Probability Convergence Rates for Sums of Independent Random Variables
- 1 January 1966
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 18, 656-665
- https://doi.org/10.4153/cjm-1966-066-x
Abstract
Let ﹛Xj,j = 1, 2, 3, …﹜ be a sequence of independent, non-degenerate random variables and write Under quite a diverse variety of conditions we may obtain as n → ∞ for all x, — ∞ < x < ∞, and some real p ⩾ 0. For example, suppose the ﹛Xj﹜ happen to be distributed identically and belong to the domain of normal attraction of a symmetric stable law with characteristic exponent α, 0 < α ⩽ < 2, α ≠ 1.Keywords
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