While distribution networks (DNs) turn from consumers to active and responsive intelligent DNs, the question of how to represent them in large-scale transmission network (TN) studies is still under investigation. The standard approach that uses aggregated models for the inverter-interfaced generation and conventional load models introduces significant errors to the dynamic modeling that can lead to instabilities. This paper presents a new approach based on quantile forecasting to represent the uncertainty originating in DNs at the TN level. First, we aquire a required rich dataset employing Monte Carlo simulations of a DN. Then, we use machine learning (ML) algorithms to not only predict the most probable response but also intervals of potential responses with predefined confidence. These quantile methods represent the variance in DN responses at the TN level. The results indicate excellent performance for most ML techniques. The tuned quantile equivalents predict accurate bands for the current at the TN/DN-interface, and tests with unseen TN conditions indicate robustness. A final assessment that compares the MC trajectories against the predicted intervals highlights the potential of the proposed method.