Climate change and its relationship to temperature are critical factors affecting glaciers, especially when populations depend on these ice reservoirs. The use of the precipitation-runoff coefficient in semi-arid, mountainous regions that are fed by glaciers can lead to important findings about how glacial melt responds to climate change. This study analyzed 40 years of monthly and annual precipitation and runoff data (1970-2009) from four sub-basins of the Elqui River (29 degrees 27' - 30 degrees 34' S and 71 degrees 22' - 69 degrees 52' W), in the Coquimbo region of Chile. The Elqui basin has a rain-snow-glacial melt regime. The areal average rainfall was estimated using the Thiessen polygon method. Gumbel and Goodrich probability distribution functions and the Log-Normal Probability Density Function (PDF) were used to understand the temporal behavior of precipitation and streamflow. The data-time behavior and PP Q(-1) coefficients were also analyzed. And the Mann-Kendall (MK) test was used to compare the results. No trends were found for flow, while a negative trend in rainfall was identified. The summer flows were notable, which remained constant. In spite of the differences between the PP Q(-1) coefficient and the MK test, the flow clearly does not come from rainfall but rather from glacial melt.