The zero-and-plus/minus-one inflated extended-Poisson distribution

Area of Science:

• Statistics
• Probability Theory
• Econometrics

Background:

• Count data frequently exhibit excess zeros or ones, posing challenges for standard Poisson models.
• Existing zero-inflated and one-inflated models may not adequately capture data with both excess zeros and ones, or negative counts.

Purpose of the Study:

• Introduce a new flexible distribution for count data, termed the "[Distribution Name]" distribution.
• Extend the capabilities of existing zero-and-one-inflated Poisson distributions.
• Provide a robust statistical tool for analyzing count data with complex zero/one inflation patterns.

Main Methods:

• Define the novel [Distribution Name] distribution and derive its key probabilistic properties.
• Investigate methods for parameter estimation within the proposed distribution framework.
• Conduct simulation studies to evaluate the performance and accuracy of the estimation techniques.

Main Results:

• The proposed [Distribution Name] distribution demonstrates flexibility in modeling count data with excess zeros, ones, and minus ones.
• Parameter estimation methods are shown to be effective through simulation experiments.
• The distribution's practical utility is validated using a real-world dataset of football scores.

Conclusions:

• The [Distribution Name] distribution offers a valuable alternative for analyzing specialized count data.
• The developed estimation techniques provide reliable parameter estimates for the new distribution.
• This work contributes a new tool for statistical modeling in fields with excess zero/one-inflated count data.