Entropy-Based Evidence Functions for Testing Dilation Order via Cumulative Entropies

Area of Science:

• Statistics
• Information Theory

Background:

• Traditional statistical methods for comparing probability distributions can be limited, particularly with complex or heavy-tailed data.
• Existing approaches like Kullback-Leibler discrepancies may not always capture nuanced distributional differences effectively.

Purpose of the Study:

• To develop novel non-parametric entropy-based evidence functions and test statistics.
• To assess the dilation order of probability distributions using cumulative residual entropy and cumulative entropy.
• To provide a robust, entropy-driven alternative for quantifying statistical evidence and stochastic ordering.

Main Methods:

• Introduction of non-parametric entropy-based evidence functions and test statistics.
• Development within a rigorous evidential framework.
• Establishment of asymptotic distributions for large-sample inference.
• Utilizing cumulative residual entropy and cumulative entropy.

Main Results:

• The proposed methods are explicitly tuned for distributional variability and stochastic ordering.
• Demonstrated robustness and high statistical power through Monte Carlo simulations.
• Effective performance across diverse distributional scenarios, including heavy-tailed models.
• Real-data example showcasing practical utility and sharper statistical evidence.

Conclusions:

• The novel entropy-based procedures offer a compelling non-parametric alternative for statistical inference.
• These methods advance the theoretical foundation of evidential statistics.
• Opens new avenues for applying cumulative entropies to a wider range of stochastic inference problems.