A new regression model for bounded response variable: An alternative to the beta and unit-Lindley regression models

Area of Science:

• Statistics
• Probability Theory
• Econometrics

Background:

• Modeling data on the (0,1) interval is crucial in various scientific fields.
• Existing distributions like the beta and unit-Lindley distributions have limitations.
• There is a need for flexible and tractable distributions for bounded data.

Purpose of the Study:

• Introduce a new probability distribution defined on the (0,1) interval.
• Derive key mathematical properties including moments and quantile functions.
• Develop and evaluate a new regression model for bounded response variables.

Main Methods:

• Analytical derivation of probability density function (PDF), cumulative distribution function (CDF), moments, and quantile function.
• Application of four parameter estimation techniques.
• Simulation studies to assess parameter estimation efficiency.
• Development of a novel regression model for bounded data.

Main Results:

• The proposed distribution exhibits simple functional forms for its PDF and CDF.
• Explicit expressions for moments, incomplete moments, and the quantile function were obtained.
• A simulation study compared the performance of four parameter estimation methods.
• The new regression model demonstrated competitive performance against established models.

Conclusions:

• The newly proposed distribution is mathematically tractable and offers desirable properties.
• The derived analytical results facilitate its practical application.
• The new regression model provides a valuable alternative for analyzing bounded response data.