Zero-inflated Bell regression models for count data.

Area of Science:

• Statistics
• Biostatistics

Background:

• Zero-inflated models are commonly used for count data with excess zeros.
• Existing models may not always capture the underlying data structure effectively.

Purpose of the Study:

• To introduce a novel zero-inflated Bell regression model for count data.
• To provide a simple yet effective alternative to existing zero-inflated regression models.
• To assess the model's performance and utility in practical scenarios.

Main Methods:

• Development of the zero-inflated Bell family of distributions.
• Application of the maximum likelihood method for parameter estimation.
• Utilizing Pearson residuals, global, and local influence methods for model diagnostics.

Main Results:

• The maximum likelihood method is effective for estimating zero-inflated Bell regression parameters.
• The proposed model demonstrates suitability for count data, including an application to infected blood cell counts.
• The new model shows better appropriateness for the considered count data compared to familiar alternatives.

Conclusions:

• The zero-inflated Bell regression model is a valuable addition to the statistical toolkit for count data analysis.
• The model provides a robust framework for inference and diagnostics.
• Its practical application highlights its potential for real-world data analysis in various fields.