Abstract:
A new statistic called “generalized sample range” is introduced and estimation of its expectation is provided. Maximum value of expectation of new range is determined. Characterization of corresponding distribution, which affords that maximum is obtained. The asymptotic behavior and limiting relations of the distribution and its characterization are considered.
Keywords:order statistics, sample range, selection differential, characterization of distributions, bounds for ordered random variables, limiting distribution, generalization of sample range.
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