Using a Machine-Trained Model that provides an Estimated Time-of-Arrival and Distribution Parameters

A technique generates estimated time-of-arrival (ETA) information to assist in navigating from one physical location to another. The technique uses a computer-implemented route-finding engine to identify a route between a specified starting location and an ending location of a trip. The route includes a sequence of segments. The technique then uses a machine-trained model to map information regarding the segments to ETA information. The ETA information provides an estimate of a time-of-arrival for the trip as a whole. The ETA information also provides an estimate of parameters that describe the level of confidence of the time-of-arrival estimate for the trip. A training system produces the machine-trained model using a loss function, part of which models the time-of-arrival for the trip as a mixture of distributions.