DOI: 10.1109/acssc.2004.1399583
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Abstract: The nonlinear estimate, due to R. A. Fisher, of the mean of a uniformly-distributed random variable given by the average of the extreme values of N samples is unbiased. Furthermore, the variance of the estimate is very much less than that for the conventional linear estimate. Two extreme-based estimates of variance are considered, and their properties investigated for uniform, Gaussian and Laplacian distributions.

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