Nonrecurring congestion creates significant delay on freeways in urban areas, lending importance to the study of facility reliability. In locations where traffic detectors record and archive data, approximate probability distributions for travel speed or other quantities of interest can be determined from historical data; however, the coverage of detectors is not always complete, and many regions have not deployed such infrastructure. This paper describes procedures for estimating such distributions in the absence of this data, considering both supply-side factors (reductions in capacity due to events such as incidents or poor weather) and demand-side factors (such as daily variation in travel activity). Two demonstrations are provided: using data from the Dallas metropolitan areas, probability distributions fitting observed speed data are identified, and regression models developed for estimating their parameters. The application of the demand-side procedure is seen to improve the accuracy of the prediction. The second demonstration, using data from the Seattle metropolitan area, identifies the appropriate capacity reduction applied to planning delay functions in the case of an incident.