<p>Count data arise frequently in diverse applied domains such as reliability engineering, survival analysis, and bio-statistics, where right censoring is often inevitable due to incomplete or partially observed outcomes. Consequently, the development of flexible discrete models capable of accommodating censored observations is of substantial methodological and practical interest. In this paper, we investigate parameter estimation for the Discrete Weibull- Geometric (DWG) distribution under a right-censoring mechanism. Inference for the model parameters is carried out using both maximum likelihood and Bayesian frameworks. We further extend the DWG distribution to a regression setting that incorporates covariate information in the presence of right-censored data. The proposed DWG regression model provides a unified and flexible framework for modeling heterogeneous and over-dispersed censored count data. The performance and adaptability of the proposed methods are assessed through extensive simulation studies and applications to real datasets. Comparative analyses demonstrate that the DWG-based models perform competitively and, in many cases, outperform commonly used discrete count models, including the Discrete Weibull, Poisson, and Negative Binomial distributions, particularly in scenarios involving censoring and over-dispersion.</p>