A multivariate correlated poisson generalized inverse gaussian regression model for dependent count data: Estimation and testing procedures

). The proposed framework provides a practical and flexible tool for analyzing correlated, overdispersed multivariate counts in public health and related domains. The highlights of this research are: • The MCPGIGR model introduces a correlated multivariate count regression framework with exposure adjustment. • It provides robust parameter estimation and hypothesis testing via MLE and MLRT. • MCPGIGR demonstrates improved model fit and practical interpretability in public health applications.