A Novel Version of the Arcsine-Rayleigh Distribution with Entropy Measures, Statistical Inference, and Applications

Area of Science:

• Statistics
• Probability Theory
• Information Theory

Background:

• Reliability and proportion data often exhibit limitations.
• Existing distributions may not fully capture the characteristics of bounded data.
• Entropy measures are crucial for understanding data uncertainty.

Purpose of the Study:

• Introduce a novel statistical distribution for bounded data.
• Explore the application of the proposed distribution in reliability and information theory.
• Analyze the probabilistic and information-theoretic properties of the new distribution.

Main Methods:

• Developed the Unit Arcsine-Rayleigh distribution (UASRD) via exponential transformation.
• Derived key statistical functions (density, cumulative, quantile, reliability, hazard, moments).
• Employed maximum likelihood, maximum product spacing, and Bayesian estimation for parameter estimation.

Main Results:

• The UASRD is shown to be a versatile model for limited reliability and proportion data.
• Entropy-based measures quantify the uncertainty and information content of the UASRD.
• Monte Carlo simulations assessed the performance of parameter estimators.
• Real-data application demonstrated the model's utility for bounded data analysis.

Conclusions:

• The UASRD provides a valuable tool for analyzing bounded data in statistics and reliability engineering.
• The study highlights the model's potential in information-theoretic applications.
• The derived statistical properties and estimation methods support its practical use.