The Best Bounds for Range Type Statistics
Tsung-Lin Cheng, Chin-Yuan Hu
TL;DR
This paper establishes the tightest possible bounds for inequalities involving range statistics in both one-variable and bivariate cases, advancing the theoretical understanding of these statistical measures.
Contribution
It provides the best possible bounds for two key inequalities related to range statistics, covering both univariate and bivariate scenarios.
Findings
Derived optimal bounds for one-variable range inequalities.
Extended bounds to bivariate range statistics.
Enhanced theoretical framework for range-based inequalities.
Abstract
In this paper, we obtain the upper and lower bounds for two inequalities related to the range statistics. The first one is concerning the one-variable case and the second one is about the bivariate case.
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Taxonomy
TopicsStatistical Methods and Inference · Advanced Statistical Methods and Models · Bayesian Methods and Mixture Models