In this work, we develop a statistical methodology to characterize solar radiation and ambient temperature from real measurements. These parameters determine the behavior of solar energy in a particular location and they are essential to establish the performance of different systems that use this type of energy, such as photovoltaic or solar-thermal systems. Since these ambient parameters have a random behavior and they cannot be controlled by human intervention over the earth's surface, a methodology to obtain a probability density distribution for twelve (12) hours a day (from 6:00 a. m to 6:00 p. m.) was built so as to predict solar energy behavior. From these density functions, corresponding cumulative probability functions are calculated. In the cases where variables cannot be deterministically determined, a numerical-best polynomial representation is found. The cumulative probability functions obtained in this work can be used as a basis to constructing statically reliable predictions of performance for different solar energy-based systems. These systems may serve as a first energy resource by using stochastic methods like Montecarlo simulations. As an example, in this paper we take data from measurement campaigns conducted in Bogotá to explain the aforementioned methodology. Finally, expressions that characterize the corresponding radiation and ambient temperature for each hour (from a statistically reliable random number between 0 and 1) are shown.