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This paper proposes and solves a mathematical model to predict the behavior of precipitation in the city of Tunja. For this, pluviometric information was subjected to fitting tests to probability distribution functions, finding the Gumbel function as the optimal one. Then, by means of mathematical treatments that use this distribution and applying the multiple linear regression method, the relationship between intensity, duration and frequency of precipitation (IDF) was determined. With the established model, the IDF curves were plotted for different return periods, depending on the duration of the precipitation event. The previous procedure was applied to the data of four stations that affect the basin that crosses the city of Tunja, generating fundamental information for the decision making in the design of engineering works and in the prevention of disasters. [ABSTRACT FROM AUTHOR]