This study provides important insights into the contemporary literature on the evolution of new probability distributions. We utilize a proven trigonometric-oriented probabilistic method to develop a new probability distribution. The distribution we suggest signifies a possible alteration of the generalized Rayleigh distribution and is referred to as the cosine generalized Rayleigh (CG-Rayleigh) distribution. We obtain various mathematical characteristics related to the CG-Rayleigh distribution. Moreover, we provide the mathematical expressions for determining the parameters of the CG-Rayleigh distribution. We also perform simulation studies with different parameter settings to illustrate the performance of these estimators. Finally, we illustrate the practical use of the CG-Rayleigh distribution by applying it to a real-world data set from the hydrology sector, particularly focusing on precipitation data to emphasize its real-world significance. To evaluate the performance of the CG-Rayleigh distribution compared to other probability distributions, we investigate various competing distributions as possible alternatives for the precipitation data. By employing four well-defined evaluation criteria, we observe that the CG-Rayleigh distribution produces better outcomes compared to its rivals. As a result, our findings show that the CG-Rayleigh distribution is a significant addition to the class of probabilistic methods for modeling data related to the hydrological cycle.