Modelling the Proportions with Excessive Endpoints Based on a Generalized Lindley Binomial Model.

Area of Science:

• Statistics
• Probability Theory
• Statistical Modeling

Background:

• Proportional data often exhibit excessive observations at endpoints (0 or 1).
• Existing binomial models may not adequately capture these endpoint phenomena or varying dispersion levels.
• Novel statistical distributions are needed for flexible analysis of such data.

Purpose of the Study:

• Introduce the generalized Lindley binomial (GLB) distribution.
• Develop statistical inference methods for the GLB model, including regression.
• Evaluate the GLB model's performance and practical utility.

Main Methods:

• The GLB distribution is constructed by compounding the binomial distribution with a generalized three-parameter Lindley distribution.
• Probabilistic properties (PMF, moments, mean, variance, MGF, dispersion index) are derived.
• Likelihood-based inference is implemented using Fisher scoring and Expectation-Maximization (EM) algorithms, including a penalized EM for stability.
• Model diagnostics utilize Pearson, deviance, and randomized quantile residuals.

Main Results:

• The GLB distribution demonstrates flexibility in modeling under- and over-dispersed data, as well as unimodal and bimodal shapes.
• Simulation studies confirm the performance of the estimation procedures.
• The GLB regression model provides a superior fit to the whitefly dataset compared to existing models.

Conclusions:

• The generalized Lindley binomial distribution is a valuable new tool for analyzing proportional data, especially with endpoint inflation.
• The developed inference methods, including penalized EM, are effective for parameter estimation.
• The GLB regression model offers enhanced performance for real-world proportional data analysis.