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Chebyshev type inequalities by means of copulas
Sever S Dragomir1,2, Eder Kikianty3
1College of Engineering and Science, Victoria University, PO Box 14428, Melbourne, VIC 8001 Australia.
Journal of Inequalities and Applications
|November 21, 2017
Summary
This study introduces Chebyshev-type inequalities derived using copulas, which are functions that link bivariate distributions to their marginals. These novel inequalities offer new analytical tools in probability and statistics.
Area of Science:
- Probability Theory
- Mathematical Statistics
- Statistical Distributions
Background:
- Copulas are essential for modeling multivariate dependencies.
- Understanding the relationship between joint and marginal distributions is crucial in statistical analysis.
- Chebyshev-type inequalities provide bounds on probabilities, offering insights into distribution behavior.
Purpose of the Study:
- To derive novel Chebyshev-type inequalities.
- To demonstrate the utility of copulas in establishing these inequalities.
- To extend the application of copula theory in probability.
Main Methods:
- Utilizing the properties of copula functions.
- Applying mathematical derivations to construct Chebyshev-type inequalities.
- Analyzing the linkage between bivariate and marginal distribution functions.
Main Results:
- Successfully obtained new Chebyshev-type inequalities.
- Demonstrated that copulas provide an effective framework for deriving such inequalities.
- Established theoretical bounds with potential applications in statistical modeling.
Conclusions:
- Copulas offer a powerful methodology for developing probability inequalities.
- The derived inequalities contribute to the theoretical foundation of statistical analysis.
- This work opens avenues for further research in copula-based statistical inference.
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