Various methods have been developed to enhance the energy efficiency of the electricity infrastructure. Demand Response (DR) is considered as the most cost-effective and reliable solution for the smoothing the demand curve when the system is under stress. DR refers to a procedure that is applied to motivate changes in the customers' power consumption habits, in response to incentives regarding electricity prices. In this paper, a novel stochastic optimization framework is presented to model the day-ahead load profile of a Residential Energy Hub (REH). Thereafter, using incentive-based DR programs through a distributed approach, the load profile of the REH becomes smoother by taking the related aggregator's desirable load profile limits into account. The applicability of the proposed framework is demonstrated by applying it to a system with one residential feeder and its related aggregator.