Mathematical analysis demonstrates Shannon entropy monotonicity in circular distributions, indicating analytical advantages over the von Mises distribution.
Key Points
To derive an analytical expression for the Shannon entropy of the cardioid distribution and examine its properties relative to the von Mises distribution.
Formulated a closed-form mathematical expression for the Shannon entropy of the circular cardioid distribution.
Analyzed the monotonicity of the derived entropy metric across its distributional parameter range.
Evaluated the analytical and computational convenience of the expression in comparison to the von Mises distribution entropy.
The derived Shannon entropy for the cardioid distribution demonstrates strict monotonicity across its parameter domain.
The cardioid entropy provides greater analytical tractability and computational convenience than the standard formulation for the von Mises distribution.