Robust regression for count data based on the Bell distribution

Abstract

Abstract In this paper, we propose a robust regression framework for the discrete one-parameter Bell distribution, a flexible count model arising from a multiple Poisson process. Since maximum likelihood estimation is highly sensitive to outliers, then we develop robust alternatives using M-, S-, and MM-estimators. These alternative methods provide resistance to contamination while retaining efficiency under clean data. Estimating equations and residual-based diagnostics are derived to support model assessment. Simulation studies show that the robust Bell regression achieves lower bias and mean squared error than classical approaches in contaminated samples. Real data applications further confirm its practical advantages. This work introduces the first robust extension of the Bell regression model, offering a reliable tool for count data analysis under irregular conditions.