An extreme limit theorem for dependency bounds of normalized sums of random variables

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Abstract

Dependency bounds are lower and upper bounds on the probability distribution of functions of random variables when only their marginal distributions are known. Using the properties of T-conjugate transforms, we show that dependency bounds for normalized sums of random variables converge to step functions as the number of summands increases. The step functions are positioned at points, depending only on the extremes of the supports of the summands' distribution functions.

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    This work was supported by a grant from the Australian Research Grants Scheme and by a Commonwealth Postgraduate Research Award scholarship.

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