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A new generalized Lindley binomial (GLB) distribution effectively models proportional data with endpoint issues. This flexible statistical model offers improved analysis for various data dispersions and shapes.

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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.