The distribution of traffic speed is a critical input in many practical transportation planning and management applications. Accurate estimation of speed distributions facilitates the understanding of traffic patterns, the evaluation of roadway performance, and the development of effective traffic control strategies. However, given the dynamic nature of traffic conditions, particularly on arterials typified by multimodal speed distributions, modeling of the distribution of traffic speed can be challenging. In this study, we propose a novel approach using XGBoostLSS, a tree-based model, for the simultaneous prediction of percentile speeds on urban arterials for each hour of the day. The model was trained and tested on a comprehensive data set, encompassing various urban arterial characteristics, traffic volume, and historical GPS-probe speed data. Our XGBoostLSS demonstrated good accuracy on percentile speed prediction compared with other approaches in literature. Also, the study identified crucial predictor variables influencing speed predictions, including speed limit, signal and stop sign density, peak capacity, right shoulder width, segment length, and crash history. Positive relationships were observed between speed limit, peak capacity, right shoulder width, segment length, and traffic speed, while increased signal and stop sign density and directional hourly traffic volume were associated with decreased traffic speed. Also, our model interpretation suggests that a minimum signal or stop sign spacing of 0.2 mi tended to improve traffic speed. The results from this study offer valuable insights for transportation professionals in estimating urban arterial traffic speed distributions, facilitating effective traffic management, and improving roadway safety.