Type I multivariate zero-inflated COM-Poisson regression model

Area of Science:

• Statistics
• Probability Theory
• Statistical Modeling

Background:

• Count data frequently exhibit excess zeros, posing challenges for standard statistical models.
• Existing zero-inflated models may not fully capture the complexities of multivariate count data.
• The Conway-Maxwell-Poisson distribution offers flexibility for modeling count data with varying dispersion.

Purpose of the Study:

• To introduce and develop the Type I multivariate zero-inflated Conway-Maxwell-Poisson (MZI-CMP) distribution.
• To explore the theoretical properties of the novel MZI-CMP distribution.
• To propose a regression framework utilizing the MZI-CMP distribution for analyzing multivariate count data with excess zeros.

Main Methods:

• Extension of the Type I multivariate zero-inflated Poisson distribution.
• Derivation of key statistical properties of the MZI-CMP distribution.
• Development of a regression model incorporating the MZI-CMP distribution.
• Model selection using Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC).

Main Results:

• The proposed Type I MZI-CMP distribution was successfully developed and its properties elucidated.
• A regression model based on the Type I MZI-CMP distribution was formulated.
• Application to two real-world datasets demonstrated the model's utility.
• The Type I MZI-CMP distribution showed superior performance in fitting multivariate count data with excess zeros compared to existing models.

Conclusions:

• The Type I multivariate zero-inflated Conway-Maxwell-Poisson distribution provides a robust and flexible tool for analyzing multivariate count data characterized by an excess of zero counts.
• The developed regression model and model selection criteria (AIC, BIC) facilitate practical application and comparison with other statistical approaches.
• The study highlights the potential of the MZI-CMP distribution in various fields dealing with zero-inflated count data.