A model for bimodal rates and proportions

Area of Science:

• Statistics
• Probability Theory
• Statistical Modeling

Background:

• The beta distribution is a standard for unit interval data.
• The standard beta distribution fails to capture bimodal patterns in unit interval data.
• Existing models lack flexibility for bimodal unit interval data.

Purpose of the Study:

• To introduce a novel bimodal beta distribution.
• To address the limitations of the standard beta distribution for bimodal data.
• To develop a flexible statistical model for unit interval data with two modes.

Main Methods:

• Construction of the bimodal beta distribution using an alpha-skew-normal approach.
• Analysis of key properties: bimodality, moments, entropies, and identifiability.
• Development of a new regression model incorporating the bimodal beta distribution.
• Maximum likelihood estimation for model parameters.
• Monte Carlo simulations to assess estimator performance.

Main Results:

• The proposed bimodal beta distribution successfully models unit interval data with two modes.
• The distribution exhibits desirable statistical properties, including bimodality and identifiability.
• Maximum likelihood estimation provides reliable parameter estimates.
• Monte Carlo experiments demonstrate good finite sample performance of the estimators.

Conclusions:

• The proposed bimodal beta distribution offers a statistically sound and flexible alternative for modeling bimodal unit interval data.
• The associated regression model enhances the applicability of this distribution in practical data analysis.
• The study validates the model's competence through simulations and a real-world data application.