TL;DR
This paper introduces a new family of exact upper bounds that smoothly interpolate between Chebyshev's and Cantelli's inequalities, providing a unified approach to bounding probabilities.
Contribution
It presents a novel family of bounds that generalize and connect Chebyshev's and Cantelli's inequalities in a unified framework.
Findings
Derived a family of bounds that interpolate between Chebyshev and Cantelli.
Proved the bounds are exact and tight under certain conditions.
Provides a new tool for probability bounds in statistical analysis.
Abstract
A family of exact upper bounds interpolating between Chebyshev's and Cantelli's is presented.
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Taxonomy
TopicsMathematical Inequalities and Applications · graph theory and CDMA systems · Graph Labeling and Dimension Problems