  In this paper, we propose the application of shrinkage strategies to estimate
coefficients in the Bell regression models when prior information about the
coefficients is available. The Bell regression models are well-suited for
modeling count data with multiple covariates. Furthermore, we provide a
detailed explanation of the asymptotic properties of the proposed estimators,
including asymptotic biases and mean squared errors. To assess the performance
of the estimators, we conduct numerical studies using Monte Carlo simulations
and evaluate their simulated relative efficiency. The results demonstrate that
the suggested estimators outperform the unrestricted estimator when prior
information is taken into account. Additionally, we present an empirical
application to demonstrate the practical utility of the suggested estimators.
