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Order of magnitude of the concentration function


Author: Peter Hall
Journal: Proc. Amer. Math. Soc. 89 (1983), 141-144
MSC: Primary 60F99; Secondary 60E99, 60G50
DOI: https://doi.org/10.1090/S0002-9939-1983-0706528-9
MathSciNet review: 706528
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Abstract: Suppose a sum of independent random variables, when scaled in a suitable way, is stochastically compact. It is proved that the precise order of magnitude of the concentration function of the sum equals the inverse of the scale factor.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0706528-9
Keywords: Concentration function, independent, median, norming constants, order of magnitude, sums of random variables
Article copyright: © Copyright 1983 American Mathematical Society