This paper introduces a new family of discrete distributions, and investigates some of their statistical properties. The geometric distribution is utilized as a baseline for this new family, resulting in the derivation of a new discrete distribution, termed the generalized geometric distribution. This new distribution exhibits a wider range of shapes in its probability mass function and hazard rate function than the geometric distribution. Several mathematical properties of the proposed model are derived, and three estimation methods, namely maximum likelihood, moments, and proportion estimation, are employed to determine estimators for the new model. The performance of these estimators is evaluated using simulated data sets, demonstrating their accuracy and reliability in estimating the parameters of the generalized geometric distribution. The proposed model is applied to a real data set, and its flexibility in fitting the data is compared to other well-known discrete distributions in the literature. Our results suggest that the generalized geometric distribution provides a better fit for the data than the existing models.