The Poisson regression model (PRM) is the standard statistical method of analyzing count data, and it is estimated by a Poisson maximum likelihood (PML) estimator. Such an estimator is affected by outliers, and some robust Poisson regression estimators have been proposed to solve this problem. PML estimators are also influenced by multicollinearity. Biased Poisson regression estimators have been developed to address this problem, including Poisson ridge regression and Poisson almost unbiased ridge estimators. However, the above mentioned estimators do not deal with outliers and multicollinearity problems together in a PRM. Therefore, we propose two robust ridge estimators to deal with the two problems simultaneously in the PRM, namely, the robust Poisson ridge regression (RPRR) estimator and the robust Poisson almost unbiased ridge (RPAUR) estimator. Theoretical comparisons and Monte-Carlo simulations are conducted to investigate the performance of the proposed estimators relative to the performance of other approaches to PRM parameter estimation. The simulation results indicate that the RPAUR estimator outperforms the other estimators in all situations where both problems exist. Finally, real data are used to confirm the results of this paper. K E Y W O R D S mean squared error, Monte-Carlo simulations, multicollinearity, outliers, robust Poisson almost unbiased ridge regression estimator, robust Poisson ridge regression estimator 1 INTRODUCTION The Poisson regression model (PRM) is the most widely used model for analyzing count data. Poisson maximum likelihood (PML) estimators for PRMs are implemented via the iterative weighted least square (IWLS) algorithm. PML estimators are affected by outliers, and some researchers have provided robust estimators for PRMs to address this problem, such as Cantoni and Ronchetti 1 and Hosseinian and Morgenthaler. 2 However, when multicollinearity occurs among the explanatory variables in the PRM, the PML estimator cannot estimate unknown regression parameters well. Different biased estimators have been suggested to solve this problem in the PRM, such as the Poisson ridge regression (PRR) estimator, 3 the Poisson Liu estimator, 4 the Poisson ridge-type estimator, 5 and the Poisson modified ridge-type estimator. 6 Furthermore, the Poisson almost unbiased ridge (PAUR) estimator is introduced by Türkan and Özel. 7 The mean squared error (MSE) properties of these estimators have been examined. Moreover, authors have adopted and modified new approaches to estimating the biasing parameter k, which is given in many studies. For more details, see Månsson and Shukur, 3 Türkan and Özel, 7 and Qasim et al. 8The PRM is a popular model used for analyzing count data in cases where the distribution of the dependent variable (y i ) is Poisson (𝜇 i ) such that 𝜇 i (𝛽) = exp (x i 𝛽), where x i is the ith row of the X matrix (which is an n × (p + 1) data matrix with p number of explanatory variables), and 𝛽 is