Statistical Synthesis of Heckman-Based Selection with Conway-Maxwell-Poisson Probability Models

This research elucidates the theoretical derivation and statistical foundations of the integrated HeckCOMPoisson model, which synthesizes the Heckman selection framework with the Conway-Maxwell-Poisson probability distribution. This unified statistical approach was formulated specifically to address truncated count data subject to sample selection mechanisms. The model exhibits superior statistical properties across multiple evaluation criteria: it demonstrates excellent performance in parametric Goodness-of-Fit assessments, yields consistent maximum likelihood estimates for count data with selection bias, and efficiently parameterizes both under-dispersed and over-dispersed count distributions. A distinguishing characteristic of the HeckCOMPoisson distribution is its parametric flexibility and its robust estimation properties when modeling discrete count data with heterogeneous dispersion parameters.