Precipitation during a specific return period plays an important role in the design of hydraulic infrastructure. The traditional approach involves collecting annual maximum precipitation data from a station, then subjecting it to statistical probability distributions (PDFs), and finally selecting the one with the lowest value in a goodness-of-fit test (e.g., Kolmogorov-Smirnov). Nevertheless, this methodology assumes current data, leaving uncertainty regarding its suitability for outdated data. The aim of this study is to compare the probability density functions (e.g., Normal, Log Normal, Pearson III) with the machine learning algorithm known as Random Forest (RF) for calculating precipitation at different return periods, using the province of Arequipa in Peru as the study area, through 5 stations located in different parts of the province. This comparison was conducted using the RMSE metric in both methods to evaluate their performance, resulting in RF having a lower RMSE than PDFs in most cases in calculating precipitation for return periods of 2, 5, 10, 20, 50 and 100 years for the studied stations.