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Residual and Past Discrete Tsallis and Renyi Extropy with an Application to Softmax Function
Taghreed M Jawa1, Nahid Fatima2, Neveen Sayed-Ahmed1
1Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia.
Entropy (Basel, Switzerland)
|December 23, 2022
Summary
This study introduces new information measures, residual and past extropy, based on discrete lifetime distributions. These measures are applied to the softmax function for analyzing simulated and real data, including ARIMA modeling.
Area of Science:
- Information Theory
- Statistical Modeling
Background:
- Extropy measures quantify information uncertainty in probability distributions.
- Discrete lifetime distributions are crucial for modeling event occurrences over time.
Purpose of the Study:
- Introduce novel residual and past extropy measures for discrete lifetime distributions.
- Explore properties and relationships of these new information measures.
- Apply the measures to the softmax function for data analysis.
Main Methods:
- Definition of residual and past Tsallis and Renyi extropy for discrete distributions.
- Analysis of properties and interrelations with existing information measures.
- Application to the softmax function, a discrete probability distribution.
- Fitting real data to an Autoregressive Integrated Moving Average (ARIMA) model.
Main Results:
- Novel extropy measures derived from discrete lifetime distributions.
- Demonstration of applicability to the softmax function using simulated and real data.
- Successful fitting of real softmax data to an ARIMA model.
Conclusions:
- The proposed extropy measures offer new insights into information quantification.
- The softmax function serves as a viable discrete probability distribution for these measures.
- ARIMA modeling provides a framework for analyzing real-world data with these measures.
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