Event-Driven Average Estimation with Dispersion-Tolerant Poisson–Inverse Gaussian Approach

Overdispersion is a major problem in the context of count data analysis, and the classical Poisson regression estimators are, in general, unreliable since they imply that the mean equals its variance. In this article, an event-driven class of average estimators, which is based on the Poisson–inverse Gaussian (P-IG) regression model, is formulated to overcome this shortcoming. P-IG regression is a mixture of Poisson and inverse Gaussian regression that is modeled to deal with the overdispersion that is often found in real data. It approximates such count data by a compound distribution with a heavy-tailed inverse Gaussian component. Suggested estimators are more effective in estimating the population means in situations of overdispersion using auxiliary data in the form of covariates. The design-based framework specifies the statistical properties of proposed estimators with respect to their bias and mean squared error (MSE). To confirm the effectiveness and the strength of the suggested methodology, a reasonable amount of simulations and real-data applications are carried out, contrasting it with customary Poisson-based estimators. The results indicate that the P-IG-based estimators are superior over their counterparts. The study provides a statistically valid and practically useful breakthrough in survey sampling and count data regression that can provide researchers and practitioners with a strong alternative to classical Poisson-regression-based mean estimator procedures.