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Explicit Expressions for Most Common Entropies.
Saralees Nadarajah1, Malick Kebe1
1Department of Mathematics, Howard University, Washington, DC 20059, USA.
Entropy (Basel, Switzerland)
|March 29, 2023
Summary
This study presents new explicit formulas for common entropies across many continuous probability distributions. These findings expand the available mathematical tools for analyzing data variation.
Area of Science:
- Information Theory
- Probability and Statistics
Background:
- Entropies quantify data variation but explicit formulas are scarce.
- Existing literature lacks comprehensive expressions for common entropies.
Purpose of the Study:
- To compile a comprehensive collection of explicit entropy expressions.
- To derive new formulas for four common entropies across numerous distributions.
Main Methods:
- Systematic derivation of entropy formulas for continuous univariate distributions.
- Utilizing known special functions in the derivation process.
Main Results:
- Provided explicit expressions for four common entropies.
- Covered over sixty continuous univariate distributions.
- Most derived expressions are novel contributions to the field.
Conclusions:
- The paper offers a valuable resource for researchers needing entropy calculations.
- The new explicit expressions facilitate deeper analysis of data variation.
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