Statistical Synthesis of Heckman-Based Selection with Conway-Maxwell-Poisson Probability Models
Leonard King’ora Thuo *
Kibabii University, Kenya.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: COMPoisson, HeckCOMPoisson, integrated, heckman