Abstract
The paper considers, as inputs to a storage system, independent random variablesX 1,X 2,... which have a symmetric three-valued distribution. Expressions are obtained for the conditional expected values of (i) the adjusted range ofX 1,...X n, conditioned on the eventX 1+...+X n=0; (ii) the Hurst range ofX 1,...,X n , conditioned on essentially the same event. Numerical comparisons of these two conditioned ranges show that they are close in value unless the inputs have high kurtosis.
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References
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Warren, D. Conditioned ranges for independent symmetric three valued inflows. Stochastic Hydrol Hydraul 4, 209–216 (1990). https://doi.org/10.1007/BF01543084
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DOI: https://doi.org/10.1007/BF01543084