This dataset includes: (1) unbiased data using a novel non-stationary bias adjustment methodology specifically tailored for environmental variables exhibiting sporadic events characterized by substantial intensity variability; (2) the parameters of the non-stationary probability distributions using marinetools.temporal. The methodology involves establishing a probability threshold to adapt the occurrence of precipitation events and employing a non-stationary theoretical and parametric quantile mapping to adjust associated biases. The dataset is part of the results obtained after the application of the methodology to daily precipitation projections from seven regional climatic models of the RCP 8.5 scenario spanning 2006-2100, alongside historical concurrent data from projections and observations spanning 1970-2005. Its efficacy is compared a widely used quantile mapping method, revealing notable differences in the performance of the methods concerning the distribution of events throughout the year and the behaviour of mean and extreme intensity values. The proposed method demonstrates promising potential in reducing uncertainty associated with systematic errors in inter-annual precipitation variability. This bears significance in evaluating hydrological responses and its associated impacts particularly in semi-arid mountainous basins.