A new two-parameter over-dispersed discrete distribution with mathematical properties, estimation, regression model...

Area of Science:

• Statistics
• Probability Theory
• Statistical Modeling

Background:

• Discrete probability distributions are fundamental in statistical modeling.
• Existing models may not adequately capture the complexities of dispersed count data.
• The need for flexible and accurate distributions for count data analysis persists.

Purpose of the Study:

• To introduce a novel two-parameter discrete probability distribution, the Poisson Loai Distribution.
• To explore the mathematical properties and applications of this new distribution.
• To develop and validate a count-regression model utilizing the proposed distribution.

Main Methods:

• Derivation of the Poisson Loai Distribution by mixing Poisson and Loai distributions.
• Investigation of the mathematical characteristics of the new distribution.
• Parameter estimation using the maximum likelihood estimation method.
• Simulation studies to evaluate the performance of the estimators.
• Application and validation on three real-world count datasets.

Main Results:

• The Poisson Loai Distribution was successfully derived and its properties analyzed.
• A count-regression model was formulated based on the new distribution.
• Simulation studies demonstrated the effectiveness of the maximum likelihood estimators.
• Empirical analysis showed the proposed distribution provides a better fit than competing models for dispersed count data.

Conclusions:

• The Poisson Loai Distribution is a valuable addition to the family of discrete probability distributions.
• It offers a robust and accurate alternative for modeling dispersed count data.
• The developed count-regression model provides a practical tool for data analysis.