This study endeavors to establish an simple, robust, and transparent forecasting framework that is easily deployable, computationally efficient, and adaptable across the various sectors constituting distributed integrated energy systems. Accordingly, a probabilistic day-ahead forecasting framework and its application are presented. A personalized standard load profile (PSLP) is then applied to electricity and heat demand, as well as PV generation. Furthermore, it is extended to incorporate a quantile personalized standard load profile employing quantile regression. Using a PCHIP interpolation, the empirical cumulative distribution function is approximated from the non-parametric approach and the probability density function derived. Furthermore, it is shown how discrete convolution can be used to determine the joint probability density function of the distributed net load. A case study was conducted at a commercial logistics facility that utilized a decentralized energy system to showcase the forecasting framework and its application for optimization in the presence of uncertainty. This involved using the net load and its probability density functions for uncertainty-based optimization.